ChemWiki - User contributions [en]

Rep:MOD:hly3614

2016-12-02T11:58:25Z

Lh3614: /* Reaction beween SO2 and the second s-cis diene fragment */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
The ENDO product turns out to be both kinetically and thermodynamically more favored as it can be reached via the lowest transition barrier among the three, and can lead to the lowest energy product as well.
 
'''Secondary Orbital Interactions'''
 
Having all of the pi systems aggregated close in space, the ENDO transition state is expected to be more sterically clashed than the EXO TS and high in energy. However, the lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The dominant secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.
 

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
The animation of IRCs illustrates that during all pathways, as the SO2 approaches close enough to the xylylene, the pi electrons in the 6-membered ring in xylylene starts to conjugate across the system and eventually the 6-membered ring becomes aromatic.
 
Besides, the IRC also indicates a concerted reaction for the chelatropic pathway, whereas the formation of C-S and C-O in both of the cycloaddition pathways are asynchronous. The reason why the formation of C-S follows the C-O bond formation is that since S atom is likely to have a larger Van der Waals' radius than O, it approaches the xylylene from a further distance than O.

=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}

Based on the calculations, the ENDO Diels-Alder Reaction is kinetically preferred as it has the lowest reaction barrier among the three pathways, while the Chelatropic product is thermodynamically most stable due to a much lower energy level of product than the others.
 
 
=== Reaction Profiles for the three possible pathways ===
[[File:Ex3 reaction profile hly dec2.png|600px|Reaction Profiles for the three possible pathways]]

=== Reaction beween SO2 and the second s-cis diene fragment ===
 
IRC For ENDO Cycloaddition
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1200x400px]]
 
 
IRC For EXO Cycloaddition
[[File: DEC2_EXTENTION_EXO_IRC_animation.gif|1200x400px]]

 
After calculating the reaction barrier and reaction energies, it turns out that both of the ENDO and EXO pathways result in high reaction barriers and higher energies of products comparing with the reactions with the outside diene substrates. Therefore the reactions with the second diene are both thermodinamically and kinetically disfavored.

=== Conclusion ===
To sum up, different calculation methods of choice using Gaussian allows us to locate (by geometry optimization and frequency calculations), visualize (by extracting the IRC) and extract various information about particular reaction pathways (by checking the MOs for HOMO-LUMO interactions) on a PES. However, the program can only make predictions based on various theoretical approximations and models in quantum mechanics, the results of which are possible to disagree with experimental observations that are affected by a lot of other factors such as solvent, temperature, pH and so on. Also, the Gaussian calculations can be time consuming because complicated calculations can be established according to the calculation methods of choice.

=== Reference ===
[1] Lecture Handout 2; Sue Gibson; 2nd year Pericyclic Reactions;
[2] [[http://www.kshitij-iitjee.com/Orbital-Hybridization-Bond-Angles]]
[3] [[http://www.kshitij-iitjee.com/Orbital-Hybridization-Bond-Angles]]

Rep:MOD:hly3614

2016-12-02T11:50:35Z

Lh3614: /* Reaction beween SO2 and the second s-cis diene fragment */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
The ENDO product turns out to be both kinetically and thermodynamically more favored as it can be reached via the lowest transition barrier among the three, and can lead to the lowest energy product as well.
 
'''Secondary Orbital Interactions'''
 
Having all of the pi systems aggregated close in space, the ENDO transition state is expected to be more sterically clashed than the EXO TS and high in energy. However, the lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The dominant secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.
 

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
The animation of IRCs illustrates that during all pathways, as the SO2 approaches close enough to the xylylene, the pi electrons in the 6-membered ring in xylylene starts to conjugate across the system and eventually the 6-membered ring becomes aromatic.
 
Besides, the IRC also indicates a concerted reaction for the chelatropic pathway, whereas the formation of C-S and C-O in both of the cycloaddition pathways are asynchronous. The reason why the formation of C-S follows the C-O bond formation is that since S atom is likely to have a larger Van der Waals' radius than O, it approaches the xylylene from a further distance than O.

=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}

Based on the calculations, the ENDO Diels-Alder Reaction is kinetically preferred as it has the lowest reaction barrier among the three pathways, while the Chelatropic product is thermodynamically most stable due to a much lower energy level of product than the others.
 
 
=== Reaction Profiles for the three possible pathways ===
[[File:Ex3 reaction profile hly dec2.png|600px|Reaction Profiles for the three possible pathways]]

=== Reaction beween SO2 and the second s-cis diene fragment ===
 
IRC For ENDO
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1200x400px]]
 
IRC For EXO
[[File: DEC2_EXTENTION_EXO_IRC_animation.gif|1200x400px]]

=== Conclusion ===
To sum up, different calculation methods of choice using Gaussian allows us to locate (by geometry optimization and frequency calculations), visualize (by extracting the IRC) and extract various information about particular reaction pathways (by checking the MOs for HOMO-LUMO interactions) on a PES. However, the program can only make predictions based on various theoretical approximations and models in quantum mechanics, the results of which are possible to disagree with experimental observations that are affected by a lot of other factors such as solvent, temperature, pH and so on. Also, the Gaussian calculations can be time consuming because complicated calculations can be established according to the calculation methods of choice.

=== Reference ===
[1] Lecture Handout 2; Sue Gibson; 2nd year Pericyclic Reactions;
[2] [[http://www.kshitij-iitjee.com/Orbital-Hybridization-Bond-Angles]]
[3] [[http://www.kshitij-iitjee.com/Orbital-Hybridization-Bond-Angles]]

File:DEC2 EXTENTION EXO IRC animation.gif

2016-12-02T11:48:38Z

Lh3614:

Rep:MOD:hly3614

2016-12-02T11:03:47Z

Lh3614: /* IRC extension */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
The ENDO product turns out to be both kinetically and thermodynamically more favored as it can be reached via the lowest transition barrier among the three, and can lead to the lowest energy product as well.
 
'''Secondary Orbital Interactions'''
 
Having all of the pi systems aggregated close in space, the ENDO transition state is expected to be more sterically clashed than the EXO TS and high in energy. However, the lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The dominant secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.
 

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
The animation of IRCs illustrates that during all pathways, as the SO2 approaches close enough to the xylylene, the pi electrons in the 6-membered ring in xylylene starts to conjugate across the system and eventually the 6-membered ring becomes aromatic.
 
Besides, the IRC also indicates a concerted reaction for the chelatropic pathway, whereas the formation of C-S and C-O in both of the cycloaddition pathways are asynchronous. The reason why the formation of C-S follows the C-O bond formation is that since S atom is likely to have a larger Van der Waals' radius than O, it approaches the xylylene from a further distance than O.

=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}

Based on the calculations, the ENDO Diels-Alder Reaction is kinetically preferred as it has the lowest reaction barrier among the three pathways, while the Chelatropic product is thermodynamically most stable due to a much lower energy level of product than the others.
 
 
=== Reaction Profiles for the three possible pathways ===
[[File:Ex3 reaction profile hly dec2.png|600px|Reaction Profiles for the three possible pathways]]

=== Reaction beween SO2 and the second s-cis diene fragment ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T11:00:24Z

Lh3614: /* Visualising reactin coordinates: IRC of The Three Possible Pathways */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
The ENDO product turns out to be both kinetically and thermodynamically more favored as it can be reached via the lowest transition barrier among the three, and can lead to the lowest energy product as well.
 
'''Secondary Orbital Interactions'''
 
Having all of the pi systems aggregated close in space, the ENDO transition state is expected to be more sterically clashed than the EXO TS and high in energy. However, the lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The dominant secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.
 

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
The animation of IRCs illustrates that during all pathways, as the SO2 approaches close enough to the xylylene, the pi electrons in the 6-membered ring in xylylene starts to conjugate across the system and eventually the 6-membered ring becomes aromatic.
 
Besides, the IRC also indicates a concerted reaction for the chelatropic pathway, whereas the formation of C-S and C-O in both of the cycloaddition pathways are asynchronous. The reason why the formation of C-S follows the C-O bond formation is that since S atom is likely to have a larger Van der Waals' radius than O, it approaches the xylylene from a further distance than O.

=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}

Based on the calculations, the ENDO Diels-Alder Reaction is kinetically preferred as it has the lowest reaction barrier among the three pathways, while the Chelatropic product is thermodynamically most stable due to a much lower energy level of product than the others.
 
 
=== Reaction Profiles for the three possible pathways ===
[[File:Ex3 reaction profile hly dec2.png|600px|Reaction Profiles for the three possible pathways]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T10:49:57Z

Lh3614: /* Visualising reactin coordinates: IRC of The Three Possible Pathways */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
The ENDO product turns out to be both kinetically and thermodynamically more favored as it can be reached via the lowest transition barrier among the three, and can lead to the lowest energy product as well.
 
'''Secondary Orbital Interactions'''
 
Having all of the pi systems aggregated close in space, the ENDO transition state is expected to be more sterically clashed than the EXO TS and high in energy. However, the lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The dominant secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.
 

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
The animation of IRCs illustrates that during all pathways, as the SO2 approaches close enough to the xylylene, the 6-membered ring in xylylene starts to conjugate across the system and eventually becomes aromatic.
 
Besides, the IRC also indicates a concerted reaction for the chelatropic pathway, whereas the formation of C-S and C-O in both of the cycloaddition pathways are asynchronous. The reason why the formation of C-S follows the C-O bond formation is that since S atom is likely to have a larger Van der Waals' radius than O, it approaches the xylylene from a further distance than O.

=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}

Based on the calculations, the ENDO Diels-Alder Reaction is kinetically preferred as it has the lowest reaction barrier among the three pathways, while the Chelatropic product is thermodynamically most stable due to a much lower energy level of product than the others.
 
 
=== Reaction Profiles for the three possible pathways ===
[[File:Ex3 reaction profile hly dec2.png|600px|Reaction Profiles for the three possible pathways]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T10:25:25Z

Lh3614: /* Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
The ENDO product turns out to be both kinetically and thermodynamically more favored as it can be reached via the lowest transition barrier among the three, and can lead to the lowest energy product as well.
 
'''Secondary Orbital Interactions'''
 
Having all of the pi systems aggregated close in space, the ENDO transition state is expected to be more sterically clashed than the EXO TS and high in energy. However, the lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The dominant secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.
 

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}

Based on the calculations, the ENDO Diels-Alder Reaction is kinetically preferred as it has the lowest reaction barrier among the three pathways, while the Chelatropic product is thermodynamically most stable due to a much lower energy level of product than the others.
 
 
=== Reaction Profiles for the three possible pathways ===
[[File:Ex3 reaction profile hly dec2.png|600px|Reaction Profiles for the three possible pathways]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T10:22:40Z

Lh3614: /* Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
The ENDO product turns out to be both kinetically and thermodynamically more favored as it can be reached via the lowest transition barrier among the three, and can lead to the lowest energy product as well.
'''Secondary Orbital Interactions'''
Having all of the pi systems aggregated close in space, the ENDO transition state is expected to be more sterically clashed than the EXO TS and high in energy. However, the lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The dominant secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.
 

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}

Based on the calculations, the ENDO Diels-Alder Reaction is kinetically preferred as it has the lowest reaction barrier among the three pathways, while the Chelatropic product is thermodynamically most stable due to a much lower energy level of product than the others.
 
 
=== Reaction Profiles for the three possible pathways ===
[[File:Ex3 reaction profile hly dec2.png|600px|Reaction Profiles for the three possible pathways]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T10:02:02Z

Lh3614: /* Secondary Orbital Interactions */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
The ENDO product turns out to be both kinetically and thermodynamically more favored as it can be reached via the lowest transition barrier among the three, and can lead to the lowest energy product as well. The reason why it is kinetically favored is interpreted by the secondary orbital interactions (more in detail in next section). However, the better thermodynamic stability of the endo product is slightly deviated from expectation. In principle, since the exo product indicates a less strained ring structure,

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}

Based on the calculations, the ENDO Diels-Alder Reaction is kinetically preferred as it has the lowest reaction barrier among the three pathways, while the Chelatropic product is thermodynamically most stable due to a much lower energy level of product than the others.
 
 
=== Reaction Profiles for the three possible pathways ===
[[File:Ex3 reaction profile hly dec2.png|600px|Reaction Profiles for the three possible pathways]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T10:00:48Z

Lh3614: /* Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
The ENDO product turns out to be both kinetically and thermodynamically more favored as it can be reached via the lowest transition barrier among the three, and can lead to the lowest energy product as well. The reason why it is kinetically favored is interpreted by the secondary orbital interactions (more in detail in next section). However, the better thermodynamic stability of the endo product is slightly deviated from expectation. In principle, since the exo product indicates a less strained ring structure,

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}

Based on the calculations, the ENDO Diels-Alder Reaction is kinetically preferred as it has the lowest reaction barrier among the three pathways, while the Chelatropic product is thermodynamically most stable due to a much lower energy level of product than the others.
 
 
=== Reaction Profiles for the three possible pathways ===
[[File:Ex3 reaction profile hly dec2.png|600px|Reaction Profiles for the three possible pathways]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T09:29:34Z

Lh3614: /* Reaction Profiles of the three possible pathways */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}

Based on the calculations, the ENDO Diels-Alder Reaction is kinetically preferred as it has the lowest reaction barrier among the three pathways, while the Chelatropic product is thermodynamically most stable due to a much lower energy level of product than the others.
 
 
=== Reaction Profiles for the three possible pathways ===
[[File:Ex3 reaction profile hly dec2.png|600px|Reaction Profiles for the three possible pathways]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T09:27:10Z

Lh3614: /* Reaction Profiles of the three possible pathways */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}

Based on the calculations, the ENDO Diels-Alder Reaction is kinetically preferred as it has the lowest reaction barrier among the three pathways, while the Chelatropic product is thermodynamically most stable due to a much lower energy level of product than the others.
 
 
=== Reaction Profiles of the three possible pathways ===
[[File:Ex3 reaction profile hly dec2.png|600px|thumb|left|Reaction Profiles for the three possible pathways]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

File:Ex3 reaction profile hly dec2.png

2016-12-02T09:24:48Z

Lh3614:

Rep:MOD:hly3614

2016-12-02T08:38:04Z

Lh3614: /* Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}

Based on the calculations, the ENDO Diels-Alder Reaction is kinetically preferred as it has the lowest reaction barrier among the three pathways, while the Chelatropic product is thermodynamically most stable due to a much lower energy level of product than the others.
 
 
=== Reaction Profiles of the three possible pathways ===

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T08:26:41Z

Lh3614: /* Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
|-
|SO2
| -0.119267
|-
|xylylene
| 0.178545
|-
|ENDO TS
| 0.090562
|-
|EXO TS
| 0.092078
|-
|Chelatropic TS
| 0.099062
|-
|ENDO PROD
| 0.021703
|-
|EXO PROD
| 0.021452
|-
|Chelatropic PROD
| 0.000001
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
'''ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]×627.5095×4.184 / KJ/mol''' '''<eq.b>'''
 
the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
| +82.14
| +86.12
| +104.45
|-
|ΔG/KJ/mol
| -98.65
| -99.31
| -155.63
|-
|}
 

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T08:04:37Z

Lh3614: /* Optimized Transition Structure at PM6 Level */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -351.77cm-1]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px|thumb|left|Vibrational frequency at TS = -334.39cm-1]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px|thumb|left|Vibrational frequency at TS = -486.71 cm-1]]
|-
|}

 

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|SO2
| -0.119267
|
|-
|xylylene
| 0.178545
|
|-
|ENDO TS
| 0.090562
|
|-
|EXO TS
| 0.092078
|
|-
|Chelatropic TS
| 0.099062
|
|-
|ENDO PROD
| 0.021703
|
|-
|EXO PROD
| 0.021452
|
|-
|Chelatropic PROD
| 0.000001
|
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 

the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
|
|
|
|-
|ΔG/KJ/mol
|
|
|
|-
|}
 

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T07:17:38Z

Lh3614: /* Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px]]
|-
|}

 
=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|SO2
| -0.119267
|
|-
|xylylene
| 0.178545
|
|-
|ENDO TS
| 0.090562
|
|-
|EXO TS
| 0.092078
|
|-
|Chelatropic TS
| 0.099062
|
|-
|ENDO PROD
| 0.021703
|
|-
|EXO PROD
| 0.021452
|
|-
|Chelatropic PROD
| 0.000001
|
|-
|}
 
Therefore, based on the computed results and the calculation methods listed in Exercise 2, eq.a and eq.b:
 
'''Calculating Reaction Barrier ΔG†:'''
'''ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 

the ΔG† and ΔG are calculated:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
! style="background: #0D4F8B; color: white;" | For Chelatropic
|-
|ΔG†/KJ/mol
|
|
|
|-
|ΔG/KJ/mol
|
|
|
|-
|}
 

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T07:03:48Z

Lh3614: /* Visualising reactin coordinates: IRC of The Three Possible Pathways */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px]]
|-
|}

 
=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}
 
 
=== Calculating the Reaction Barriers ΔG† and the Reaction Energies ΔG ===

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T06:59:22Z

Lh3614: /* Optimized Transition Structure */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure at PM6 Level ===
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | Optimized TS
|-
|EXO Cycloaddition
|[[File: Ex3_exo_ts_opt.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: Ex3_endo_ts_opt.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic ex3 ts opt.gif|1000x400px]]
|-
|}

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T05:46:04Z

Lh3614: /* Reaction Scheme */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Optimized Transition Structure ===
 
Exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]
 
Endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
 
Chelatropic optimized
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T05:40:31Z

Lh3614: /* ts opt frequency */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T05:38:32Z

Lh3614: /* IRC of The Three Possible Pathways */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== Visualising reactin coordinates: IRC of The Three Possible Pathways ===
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Reaction Pathways
! style="background: #0D4F8B; color: white;" | IRC
|-
|EXO Cycloaddition
|[[File: DEC1 HLY ex3 EXO IRC.gif|1200x400px]]
|-
|ENDO Cycloaddition
|[[File: DEC1 HLY EX3 ENDO IRC.gif|1200x400px]]
|-
|Chelatropic Reaction
|[[File: Chelatropic hly dec1 IRC.gif|1000x400px]]
|}

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T05:22:42Z

Lh3614: /* Second Orbital Interactions */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Secondary Orbital Interactions ===
The lower reaction barrier via an ENDO transition state can be explained by the secondary orbital interactions since a strong, in-phase orbital overlap is easily observed from the HOMO of the ENDO transition state. The strong secondary orbital interaction between the p orbitals on O atoms and C atoms stablizes the HOMO of the ENDO TS, lowering the activation barrier and yielding the kinetically more stable ENDO product formation.

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T04:48:03Z

Lh3614: /* Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored as it can be reached via a lower transition barrier, and can lead to a lower energy product as well.

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T04:21:59Z

Lh3614: /* Frotier Molecular Orbital ( FMO ) Analysis */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|(distorted)u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored product as it can be reached via a lower transition state, and can lead to a lower energy product as well.

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T04:16:34Z

Lh3614: /* Frontier Molecular Orbital Analysis */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored product as it can be reached via a lower transition state, and can lead to a lower energy product as well.

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T04:13:01Z

Lh3614: /* Frotier Molecular Orbital ( FMO ) Analysis */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored product as it can be reached via a lower transition state, and can lead to a lower energy product as well.

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T04:05:15Z

Lh3614: /* Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''<eq.a>'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''<eq.b>'''
 
Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}
 
Based on the comparisons, the ENDO product is proved to be both kinetically and thermodynamically more favored product as it can be reached via a lower transition state, and can lead to a lower energy product as well.

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T03:48:37Z

Lh3614: /* Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
| -701187.3133
|-
|Cyclohexadiene
| -233.324375
| -612593.0878
|-
|ENDO TS
| -500.332149
| -1313621.931
|-
|EXO TS
| -500.329168
| -1313614.105
|-
|ENDO PROD
| -500.418691
| -1313849.147
|-
|EXO PROD
| -500.417322
| -1313845.553
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)] '''{eq.a}'''
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)] '''{eq.b}'''
 

Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
| +158.47
| +166.30
|-
|ΔG/KJ/mol
| -68.75
| -65.15
|-
|}

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T03:21:58Z

Lh3614: /* Frotier Molecular Orbital ( FMO ) Analysis */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration [optimized at B3LYP/6-31G(d) level]
! style="background: #0D4F8B; color: white;" | Symmetry
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|}
 
According to the FMOs illustrated above, the HOMOs and LUMOs of both ENDO and EXO transition states are dominated by the interactions between the HOMO of 1,3-Dioxole and the LUMO of cyclohexadiene, both of which have a πu symmetry. Therefore ENDO and EXO transition states also have πu symmetries. This computed result refers to an inverse electron demand, which is likely due to the fact that being attached to two electron donating groups (i.e the O atoms ) makes 1,3-dioxole a very poor dienophile with a high energy LUMO and thus making the LUMO of dienophile and HOMO of diene too far in energy to interact.
 

=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
 
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
|
|-
|Cyclohexadiene
| -233.324375
|
|-
|ENDO TS
| -500.332149
|
|-
|EXO TS
| -500.329168
|
|-
|ENDO PROD
| -500.418691
|
|-
|EXO PROD
| -500.417322
|
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]
 

Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
|
|
|-
|ΔG/KJ/mol
|
|
|-
|}

<NOT FINISHED!!>

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T02:34:11Z

Lh3614: /* Frontier Molecular Orbital Analysis */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that lowers its LUMO energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a higher energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the unsubstituted butadiene and ethylene are not a good diene and not a good dienophile respectively to ensure the normal energy match. As for symmetry, interacting orbitals also need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|}
 
<Analyse mos!!!!!!!!>
 
=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
 
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
|
|-
|Cyclohexadiene
| -233.324375
|
|-
|ENDO TS
| -500.332149
|
|-
|EXO TS
| -500.329168
|
|-
|ENDO PROD
| -500.418691
|
|-
|EXO PROD
| -500.417322
|
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]
 

Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
|
|
|-
|ΔG/KJ/mol
|
|
|-
|}

<NOT FINISHED!!>

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T02:21:19Z

Lh3614: /* Frontier Molecular Orbital Analysis */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===
[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that raises its LUMO in energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a lower energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the butadiene and the ethylene are not a good diene and not a good dienophile respectively. As for symmetry, interacting orbitals need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|}
 
<Analyse mos!!!!!!!!>
 
=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
 
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
|
|-
|Cyclohexadiene
| -233.324375
|
|-
|ENDO TS
| -500.332149
|
|-
|EXO TS
| -500.329168
|
|-
|ENDO PROD
| -500.418691
|
|-
|EXO PROD
| -500.417322
|
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]
 

Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
|
|
|-
|ΔG/KJ/mol
|
|
|-
|}

<NOT FINISHED!!>

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T02:07:43Z

Lh3614: /* C-C Bond Length Analysis */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===

[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that raises its LUMO in energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a lower energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the butadiene and the ethylene are not a good diene and not a good dienophile respectively. As for symmetry, interacting orbitals need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. This might be due to the ring strain leading to a distortion of the bond. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|}
 
<Analyse mos!!!!!!!!>
 
=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
 
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
|
|-
|Cyclohexadiene
| -233.324375
|
|-
|ENDO TS
| -500.332149
|
|-
|EXO TS
| -500.329168
|
|-
|ENDO PROD
| -500.418691
|
|-
|EXO PROD
| -500.417322
|
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]
 

Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
|
|
|-
|ΔG/KJ/mol
|
|
|-
|}

<NOT FINISHED!!>

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T02:02:14Z

Lh3614: /* Vibration at Transition State Corresponding to Reaction Path */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===

[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that raises its LUMO in energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a lower energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the butadiene and the ethylene are not a good diene and not a good dienophile respectively. As for symmetry, interacting orbitals need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 suggests the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration mode indicates the vibrations of the two reactant molecules are rather in two parallel planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, but an IRC animation makes the idea of this concerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|}
 
<Analyse mos!!!!!!!!>
 
=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
 
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
|
|-
|Cyclohexadiene
| -233.324375
|
|-
|ENDO TS
| -500.332149
|
|-
|EXO TS
| -500.329168
|
|-
|ENDO PROD
| -500.418691
|
|-
|EXO PROD
| -500.417322
|
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]
 

Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
|
|
|-
|ΔG/KJ/mol
|
|
|-
|}

<NOT FINISHED!!>

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T01:39:00Z

Lh3614: /* C-C Bond Length Analysis */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===

[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that raises its LUMO in energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a lower energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the butadiene and the ethylene are not a good diene and not a good dienophile respectively. As for symmetry, interacting orbitals need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
[The bond lengths are measured by extracting the bond lengths of corresponding optimized structures in GaussView.]
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], and by looking at the IRC profile, the two reactants start to approach each other from a distance of ~3.41Å, which is approximately twice of the Van der Waals' radius. The computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.41Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond at the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign of the vibrational frequency actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 indicates the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration does not since the vibrations of the two reactant molecules are rather in two planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, while an IRC animation makes the idea of this conerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|}
 
<Analyse mos!!!!!!!!>
 
=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
 
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
|
|-
|Cyclohexadiene
| -233.324375
|
|-
|ENDO TS
| -500.332149
|
|-
|EXO TS
| -500.329168
|
|-
|ENDO PROD
| -500.418691
|
|-
|EXO PROD
| -500.417322
|
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]
 

Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
|
|
|-
|ΔG/KJ/mol
|
|
|-
|}

<NOT FINISHED!!>

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T01:15:48Z

Lh3614: /* C-C Bond Length Analysis */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===

[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that raises its LUMO in energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a lower energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the butadiene and the ethylene are not a good diene and not a good dienophile respectively. As for symmetry, interacting orbitals need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature values, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortend to form a double bond although the bond length is slightly shorter than expected. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of a carbon is ~1.70Å [3], the computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.40Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond during the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign of the vibrational frequency actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 indicates the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration does not since the vibrations of the two reactant molecules are rather in two planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, while an IRC animation makes the idea of this conerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|}
 
<Analyse mos!!!!!!!!>
 
=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
 
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
|
|-
|Cyclohexadiene
| -233.324375
|
|-
|ENDO TS
| -500.332149
|
|-
|EXO TS
| -500.329168
|
|-
|ENDO PROD
| -500.418691
|
|-
|EXO PROD
| -500.417322
|
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]
 

Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
|
|
|-
|ΔG/KJ/mol
|
|
|-
|}

<NOT FINISHED!!>

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-02T01:08:34Z

Lh3614: /* Frontier Molecular Orbital Analysis */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===

[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap. In the case of Fig.2, the small energy gap results from attaching an electron withdrawing group to the dienophile substrate that raises its LUMO in energy. This can be further enhanced by making the diene substrate more electron-rich, leading to a lower energy HOMO. The inconsistency of the computed results is likely to arise from the fact that the butadiene and the ethylene are not a good diene and not a good dienophile respectively. As for symmetry, interacting orbitals need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed because the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature vlues, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortened to form a double bond although the bond length is slightly shorter than expected. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of carbon is ~1.70Å [3], the computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.40Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond during the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign of the vibrational frequency actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 indicates the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration does not since the vibrations of the two reactant molecules are rather in two planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, while an IRC animation makes the idea of this conerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|}
 
<Analyse mos!!!!!!!!>
 
=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
 
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
|
|-
|Cyclohexadiene
| -233.324375
|
|-
|ENDO TS
| -500.332149
|
|-
|EXO TS
| -500.329168
|
|-
|ENDO PROD
| -500.418691
|
|-
|EXO PROD
| -500.417322
|
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]
 

Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
|
|
|-
|ΔG/KJ/mol
|
|
|-
|}

<NOT FINISHED!!>

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

Rep:MOD:hly3614

2016-12-01T23:49:13Z

Lh3614: /* IRC of The Three Possible Pathways */

== '''
== '''Introduction''' ==
=== Potential Energy Surface (PES) ===
A potential energy surface (PES) is an energy 'landscape' that interpretates the total energy of a molecule as a function of molecular geometries based on Born-Oppenheimer Approximation. According to the fact that a polyatomic molecule often has 3N-6 ( N= Number of atoms and N>2 ) geometric degrees of freedom, the PES is likely to possess 3N-6 dimensions but is usually reduced to 3-D representation.

=== A Minimum And A Transition State ===
A minimum on the PES corresponds to a stationary point where the gradient of the energy curve (i.e the first derivative) is zero and the curvature (i.e the second derivative) reflects that any change being made to this point leads to an increase of energy, whereas a transition state is a saddle point at which the change of total energy with respect to the change of geometry is zero but in terms of curvature, moving away from the point, the energy drops in one direction.
=== Relevant Gaussian Calculations ===
A geometry optimization in Gaussian helps find out the stationary points (i.e gradient=0) by calculating the first derivatives of the energy curve and the frequency calculations are used to obtain information about the curvature of the points (i.e the second derivative) by calculating harmonic frequencies of the polyatomic molecule, confirming whether a minimum or a transition state is reached, based on the fact that all the vibrational frequencies for a minimum are real numbers whereas an imaginary frequency occurs for a transition structure.

== '''Exercise 1: Reaction of Butadiene with Ethylene''' ==
=== Reaction Scheme ===
[[File: EX1 REACTION SCHEME.png|x250px|400px|]]
=== Frontier Molecular Orbital Analysis ===

[[File:Finallllll ex1 mo.png|thumb|left|x600px|600px|Fig. 1: MO Diagram of Butadiene/Ethylene TS]]
[[File:Cycloaddition_lecture_handout.PNG|thumb|left|x450px|450px|Fig. 2: MO Diagram for an example of cycloaddtion with normal electron demand [1]]]
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule and orbital:
! style="background: #0D4F8B; color: white;" | MOs:
! style="background: #0D4F8B; color: white;" | Symmetry [gerade/ungerade
(g/u for short)]:
|-
| Butadiene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 11; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 12; rotate y 120; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV29 HLY EX1 PREOPTIMIZED FRAGMENT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| u
|-
| Ethene, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; rotate y 90; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>NOV_29_ETHENE_MINIMUM_OPT_PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| g
|-
| Butadiene/ethylene Transition state, HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|-
| Butadiene/ethylene Transition state, 2nd LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02 </script>
<uploadedFileContents>NOV30 HLY EX1 TS OPT PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| n/a
|}

According to the results of Gaussian calculations, the HOMO of the transition state is formed from the LUMO of the butadiene and the HOMO of the ethylene, both of which have the πu symmetry. Theoretically, however, as illustrated in Fig 2, a Diels-Alder Reaction with normal electron demand favours the interaction between the HOMO of diene and the LUMO of the dienophile due to a smaller energy gap and better orbital overlap resulting from attaching an electron withdrawing group to the dienophile substrate that raises energy of its LUMO. The small energy gap can be further enhanced by making the diene substrate more electron-rich that lowers the energy of its HOMO. The inconsistency of the computed results is likely to arise from the fact that the butadiene and the ethylene are not a good diene and a dienophile respectively. Additionally, interacting orbitals need to have the same symmetry to allow a non-zero orbital overlap, so the g-g and u-u interactions are symmetry allowed whereas a g-u interaction is symmetry disallowed as the orbital overlap integral is equal to zero.

=== C-C Bond Length Analysis ===
'''Changes in Bond Lengths:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecule:
! style="background: #0D4F8B; color: white;" | Illustration:
! style="background: #0D4F8B; color: white;" | C-C Bond Lengths/Å:
|-
| Butadiene
|[[File:NUMBERER_BUTADIENE.png|x100px|100px|]]
| C1-C2=1.33531

C2-C3=1.46835

C3-C4=1.33531
|-
| Ethene
|[[File:Ethene.png|x80px|80px|]]
|C5-C6=1.32731
|-
| Transition State
|[[File:NUMBERED TRANSITION STATE.png|x100px|100px|]]
| C1-C2=1.37977
C2-C3=1.41110

C3-C4=1.37979

C4-C6=2.11469

C6-C5=1.38177

C5-C1=2.11479
|-
| Product
|[[File:Product 1.png|x100px|100px|]]
| C1-C2=1.50034

C2-C3=1.33766

C3-C4=1.50034

C4-C6=1.54004

C6-C5=1.54076

C5-C1=1.54003
|-
|}
 
'''Representative C-C bond lengths with respect to hybridization/Å:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | sp3-sp3
! style="background: #0D4F8B; color: white;" | sp3-sp2
! style="background: #0D4F8B; color: white;" | sp2-sp2
|-
|literature value[2]: 1.54Å
computed value: 1.54Å
|literature value[2]: 1.50Å
computed value: 1.50Å
|literature value[2]: 1.47Å
computed value: 1.47Å
(except C2=C3 in the product = 1.34Å)
|-
|}
 
By comparing the computed bond lengths with the literature vlues, the C=C double bonds (C1-C2, C3-C4, C5-C6) in both of the reactants start to elongate until eventually become single bonds in the product during the reaction, while the previous C-C single bond in butadiene (C2-C3) is shortened to form a double bond although the bond length is slightly shorter than expected. Also, based on an appropriate trajectory of the reactants, two new single bonds (C4-C6 and C5-C1) are formed with typical sp3 C-C bond lengths of 1.54Å via a transition state where the distances between the butadiene terminal carbons and the ethylene carbons are appox. 2.11Å. A typical Van der Waals' radius of carbon is ~1.70Å [3], the computed distance of 2.11Å at transition state lying in between the Van der Waals' distance of ~3.40Å and the final bond lengths of 1.54Å indicates a partially formed C-C single bond during the transition state.

=== Vibration at Transition State Corresponding to Reaction Path ===
[[File: Gif_vibration_at_transition_state_ex1.gif|1500x400px|gif 1: Imaginary vibrational frequency at transition state corresponding to reaction path: -948.57cm-1]]
 
''Gif 1'': Vibration at transition state with an imaginary vibrational frequency: -948.57cm-1
 
 
[[File: 145.10.gif|1500x400px|gif 2: first positive vibrational frequency at transition state: 145.10cm-1]]
 
''Gif 2'': vibration with first positive vibrational frequency: 145.10cm-1
 
 
 
The vibration occurring at -948.57cm-1 in the transition state is illustrated in ''Gif.1''. The negative sign of the vibrational frequency actually represents an imaginary vibrational frequency, which results from solving the square root of a negative force constant, i.e the second derivative (curvature) of the energy curve related to this particular reaction pathway. Since mathematically, a negative second derivative indicates a maximum point, in this case, the negative value occurring at -948.57cm-1 indicates the vibration of bonds corresponding to an energy maximum in the transition state.
 
 
Comparing the vibrations shown in Gif.1 and Gif.2, the vibration occurring at -948.57cm-1 shows a trend towards bond formation between the butadiene terminal carbons and ethylene carbons, whereas the lowest positive vibration does not since the vibrations of the two reactant molecules are rather in two planes without any interactions to allow a bond formation.
 
 
In addition, the illustration of the vibration at -948.57cm-1 suggests that the formation of the 2 bonds is synchronous, while an IRC animation makes the idea of this conerted reaction more evident:
 
[[File: DEC1 HLY ex1 irc.gif|1500x375px|gif 3: IRC Animation of the Diels-Alder reaction of butadiene/ethylene]]
 
''gif 3'': IRC Animation of the Diels-Alder reaction of butadiene/ethylene
 

== '''Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole''' ==
=== Reaction Scheme ===
[[File:EX2 REACTION SCHEME.png|600px|Reaction Scheme of cycloaddtion of cyclohexadiene and 1,3-Dioxole]]

 

=== Frotier Molecular Orbital ( FMO ) Analysis ===
 
'''FMOs of the reactants:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules and Orbitals
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry (g/u)
|-
|1,3-Dioxole HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|-
|1,3-Dioxole LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY ex2 dioxole OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 22; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|g
|-
|Cyclohexadiene LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 23; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>DEC1 HLY EX2 CYCLOHEXADIENE 631G OPT.log</uploadedFileContents>
</jmolApplet>
</jmol>
|u
|}
 
 
'''Illustration of FMOs during the cyclohexadiene/1,3-Dioxole transition state:'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Types of Transition States and FMOs
! style="background: #0D4F8B; color: white;" | Illustration
! style="background: #0D4F8B; color: white;" | Symmetry
|-
|ENDO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|ENDO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 34; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 ENDO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|-
|EXO LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; rotate y 30; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.01</script>
<uploadedFileContents>NOV 30 HLY EX2 EXO TS OPT 631G.log</uploadedFileContents>
</jmolApplet>
</jmol>
|N/A
|}
 
<Analyse mos!!!!!!!!>
 
=== Analysis on The Reaction Barrier ΔG† and The Reaction Energy ΔG ===
 
'''Sum of Electronic and Thermal Free Energies at each stage during the reaction'''
 
{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Molecules
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies/ Hartrees/Particle
! style="background: #0D4F8B; color: white;" | Sum of Electronic and Thermal Free Energies ×627.5095×4.184 / KJ/mol
|-
|1,3-Dioxole
| -267.068132
|
|-
|Cyclohexadiene
| -233.324375
|
|-
|ENDO TS
| -500.332149
|
|-
|EXO TS
| -500.329168
|
|-
|ENDO PROD
| -500.418691
|
|-
|EXO PROD
| -500.417322
|
|-
|}
 
*'''Unit conversion:'''
The way to convert unit from ''Hartree/particle'' to ''KJ/mol'' is by multiplying constants 627.5095 and 4.184 [4]
 
*'''Calculating Reaction Barrier ΔG†:'''
ΔG†= [GTS - (Gcyclohexadiene+ Gdioxole)]
 
*'''Calculating Reaction Energy ΔG:'''
ΔG= [GProduct - (Gcyclohexadiene+ Gdioxole)]
 

Therefore, based on the computed results and the calculation methods listed above:
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | For ENDO
! style="background: #0D4F8B; color: white;" | For EXO
|-
|ΔG†/KJ/mol
|
|
|-
|ΔG/KJ/mol
|
|
|-
|}

<NOT FINISHED!!>

=== Second Orbital Interactions ===

== Exercise 3: Diels-Alder vs Cheletropic ==
=== Reaction Scheme ===
[[File: REACTION SCHEME HLY EX3.png|x500px|600px]]

=== IRC of The Three Possible Pathways ===
exo irc
[[File: DEC1 HLY ex3 EXO IRC.gif|1500x400px]]
endo irc
[[File: DEC1 HLY EX3 ENDO IRC.gif|1500x400px]]
CHELATROPIC IRC
[[File: Chelatropic hly dec1 IRC.gif|1500x400px]]

=== ts opt frequency ===
chelatropic
[[File: Chelatropic ex3 ts opt.gif|1500x400px]]
endo
[[File: Ex3_endo_ts_opt.gif|1500x400px]]
exo
[[File: Ex3_exo_ts_opt.gif|1500x400px]]

=== IRC extension ===
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]
[[File: DEC1_EXTENTION_ENDO_IRC_animation.gif|1500x400px]]

File:Ex3 exo ts opt.gif

2016-12-01T23:48:46Z

Lh3614:

File:Ex3 endo ts opt.gif

2016-12-01T23:48:21Z

Lh3614:

File:Chelatropic ex3 ts opt.gif

2016-12-01T23:46:53Z

Lh3614:

Rep:MOD:hly3614

2016-12-01T23:25:22Z

Lh3614: /* IRC of The Three Possible Pathways */

File:Chelatropic hly dec1 IRC.gif

2016-12-01T23:24:34Z

Lh3614:

Rep:MOD:hly3614

2016-12-01T23:19:12Z

Lh3614: /* IRC of The Three Possible Pathways */

File:DEC1 EXTENTION ENDO IRC animation.gif

2016-12-01T22:33:32Z

Lh3614:

Rep:MOD:hly3614

2016-12-01T22:29:56Z

Lh3614: /* IRC of The Three Possible Pathways */

File:DEC1 HLY EX3 ENDO IRC.gif

2016-12-01T22:27:49Z

Lh3614:

File:DEC1 HLY ex3 EXO IRC.gif

2016-12-01T22:26:15Z

Lh3614:

File:NOV27 HLY ex3 ENDO TS IRC PM6.gjf

2016-12-01T22:25:12Z

Lh3614:

Rep:MOD:hly3614

2016-12-01T22:22:10Z

Lh3614: /* Vibration at Transition State Corresponding to Reaction Path */