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Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T17:00:00Z

Yz1506:

==== '''Exercise: The Diels Alder Cycloaddition''' ====

'''''

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''''

'''The Diels-Alder reaction between ethylene and butadiene'''

'''''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap siginificantly, otherwise, the reaction is forbbidden.

'''''

'''Exercise'''

The AM1 semi-empirical molecular orbital method are used for these calculations at the beginning.

'''''

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

'''''

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

'''''

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

'''''

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| '''Symmetry w.r.t plane'''
| Asymmetric
| Symmetric
|}

'''''

The above procedures have been repeated for '''ethylene''':

'''''

{| border="2"
|-
! '''Jmol of ethylene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

'''''

Plot the '''HOMO''' and '''LUMO''' of '''ethylene''' and determine its symmetry:

'''''

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Ethylene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| '''Symmetry w.r.t plane'''
| Symmetric
| Asymmetric
|}

'''''

'''ii)''' Computate the '''Transition State geometry''' and examine the nature of the reaction path for the prototype reaction.

'''''

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.

The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

'''''

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

'''''

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

'''''

Plot the '''HOMO''' and '''LUMO''' of '''transition structure''' and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene.

'''''

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

'''''

The reaction is allowed in a concerted stereospecific fashion a result of the asymmetric HOMO of cis-butadiene overlaps with the asymmetric LUMO of ethylene; the symmetric LUMO of cis-butadiene overlaps with the symmetric LUMO of ethylene; these HOMO-LUMO pair interactions forms an asymmetric HOMO of the resulting adduct consisting of two new σ bonds.

'''''

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

'''''

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''''

Sketch the endo and exo products in Gaussview -> Calculate: Gaussian -> Job list: opt+freq; once -> Method: HF/3-21G -> Submit.
Then, beased on the optimized geometries, the two conformers are optimized futher at B3LYP/6-31G(d) level of theory.

'''''

'''Results for Endo and Exo products:'''

'''''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

'''''

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

'''''

From the results obtained above, the endo product is lower in energy than the exo one and therefore endo is more favoured, the reason for this is because when the dieneophile is substituted, the π orbitals in substituents can interact with the new double bond which forms in the product, this interaction stabilises the regiochemistry of the endo form more than that of the exo form(so-called the secondary orbital overlap effect), and this effect determines which transition state conformer is more favoured.

'''''

The optimisation was carried out by using the Hessian method based on a guessed transition structure(intermolecular bond length of the chain end carbons= 2.1A), but in order to get a reasonable guessed transition struture, both cyclohexa-1,3-diene and maleic anhydride were optimized first and then combined together to give the exo and endo transition structures.

'''''

'''Results for Endo and Exo tansition states:'''

'''''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

'''''

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''''

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

'''''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

'''''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

'''''

The typical sp3 and sp2 C-C bondlengths are 1.54Å and 1.34Å respectively, the double bond in cyclohexa-1,3-diene at the transition state is 1.397Å which is somewhere in between a double and single carbon carbon bond. The van der Waal radius of carbon is 1.702Å and the bond forming distances for the endo and exo transition states are 2.16Å, 2.17Å respectively, which indicates the orbitals do not overlap significantly and hence gives rise to a transition state in this case.

The formation of the two bonds is synchronous and no similarity has been senn when compare with the lowest positive frequency.

'''''

For the reaction of cyclohexa-1,3-diene with maleic anhydride, the exo product is more strained because the bridging group and the -C=O-CO-C=O- fragment are pointing in the same direction whereas in the endo product, they are pointing away from each other.
There is only one major nodal plane has been observed which is in between the HOMO between the -C=O-CO-C=O- fragment(x-axis, in this case).

'''''

Rep:Mod:Yunzhang Module3 Writeup1

2009-02-27T16:13:36Z

Yz1506: /* '''Module3, Experiment 3: The Transition State''' */

Rep:Mod:Yunzhang Module3 Writeup2

2009-02-27T16:11:02Z

Yz1506: /* ''' Optimizing the "Chair" and "Boat" Transition Structures''' */

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

'''''

''' Optimizing the "Chair" Transition Structures'''

'''''

'''(a)''' Draw a planar allyl fragment(CH2CHCH2)-> run a HF/3-21G level optimisation -> copy this structure to a new GaussView window
twice and orient for them to look like the '''chair''' transition state (translate one fragment: Shift Alt keys + Left Mouse button;
rotate: Alt key + Left)-> Bond distance between the terminal Cs of the CH2CHCH2 fragments ~ 2.2 Å -> Save as chair_ts_guess.

'''''

'''(b)''' Use Hartree Fock and the default basis set 3-21G for parts (b) to (f).
'''Optimization by using Hessian:'''
File → New → Create MolGroup -> copy and paste the guess structure into the window -> Calculation: Gaussian -> Job Type:
Opt+Freq; Optimization to a: TS (Berny); calculate force constants: Once; Additional keyword: Opt=NoEigen -> Submit.
After the job completes, it gives an imaginary frequency '''-817.897cm-1''' due to the Cope rearrangement.

'''''

'''Optimization by using Frozen coordinate:'''
'''(c)''' Frozen coordinate optimization: File → New → Create MolGroup -> copy and paste the guess structure into the window ->
Edit: Redundant Coord Editor -> click on Create a New Coordinate -> On GaussView window: select 2 of the terminal Cs from the
CH2CHCH2 fragments which form/break a bond during the rearrangement -> On coordinate editor: select Coordination: Bond; Freeze
Coordinate -> Set value: 2.2 -> click on Create a New Coordinate -> select the opposite 2 terminal Cs -> select Bond and Freeze
Coordinate -> Click OK -> Submit.
'''(d)''' Open the file after the job has finished -> Edit: Redundant Coord Editor -> create a new coordinate by clicking on Create
a New Coordinate -> Select one of the bonds that was frozen before -> Coordinative: Bond; Derivative -> Repeat this procedure for
the other bond -> Calculate: Gaussian -> Job type: opt+freq; optimize to a: TS(Berny); Calulate Force Constants: Never ->
yun_opt_freq_redundant2 -> submit. This transition structure gives an imaginary frequency '''-817.947cm-1''' due to the Cope rearrangement.

'''''

'''Results:'''

'''''

{| border="2"
|-
! /
! '''Chair transition structure(Optimized under Hessian)'''
! '''Chair transition structure(Optimized under Redundant)'''

|-
| '''Jmol'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>blue</color><size>150</size>
<uploadedFileContents>chair_HF_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>blue</color><size>150</size>
<uploadedFileContents>RD_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| '''Result summary'''
| [[Image:chair_HF_rs.jpg|center|thumb]]
| [[Image:chair_RD_rs.jpg|center|thumb]]
|-
| '''Imaginary frequency'''
| [[Image:IM_HF.jpg|center|thumb]]
| [[Image:IM_RD.jpg|center|thumb]]
|-
| '''Geometric information(atom list)'''
| [[Image:HF_AL_CHAIR.jpg|center|thumb]]
| [[Image:RD_AL_CHAIR.jpg|center|thumb]]
|}

'''''

''' Optimizing the "Boat" Transition Structures'''

'''''

'''(e) Optimization by using the QST2 method''':
Open the chk file of anti2 -> open a second window -> create a new MolGroup -> copy anti2 molecule into the new window
and select File → New → Add to MolGroup(the original molecule disappears and a green circle appearwith a 2 next to
it -> copy and paste the reactant molecule again and we are going to make it the product molecule -> click on the
icon showing two molecules side by side -> View: select Labels and change the numbering.
'''Set up the 1st QST2 optimization:'''
On '''Gaussian''' menu -> Job Type: Opt+Freq; optimize to a: TS (QST2)-> Submit -> job fails.

'''''

{| border="2"
|-
! [[Image:fail.jpg|center|thumb]]
! [[Image:Fail_chair.jpg|center|thumb]]
! The structure looks like chair transition state but with bonds more dissociated, this is because the calculation translated the top CH3CH2CH3 fragment but did not rotate it around the central bonds.
|}

'''''

{| border="2"
|-
!'''Set up your QST2 calculation again''' by going back to the original input file and this time
modify the geometries of both molecules, for the reactant, make the central C-C-C-C dihedral angle 0
and the inside C-C-C angle 100. Repeat for the product molecule.
![[Image:sm_pd.jpg|left|thumb]]
|}

'''''

The '''QST2 calculation''' was then carried out.

'''''

'''Results:'''

'''''

{| border="2"
|-
! '''Jmol of the boat transition state under QST2 method'''
! '''Result summary'''
! '''Imaginary vibration'''
! '''Advantage and disadvantage of using the QST2 method'''

|-
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>QST2_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
| [[Image:QST2_RS.jpg|center|thumb]]
| [[Image:QST2_VB.jpg|center|thumb]]
| The QST2 method is easy to set up because it is fully automated, however the job has failed for serveal times before the correct optimisation was obtained due to the input guess transition structure is not close enough to the real one.
|}

'''''

'''Optimization by using the QST3 method''':

'''''

'''Result:'''

'''''

{| border="2"
|-
! '''Input image'''
! '''Result Summary and Imaginary vibration'''
! '''Advantage of using the QST3 method'''
|-
| [[Image:boat_2_freq_opt_QST3_importimage.jpg|center|thumb]]
| [[Image:boat_2_freq_opt_QST3_all.jpg|center|thumb]]
| The QST3 method is more reliable and the optimization is successfully carried out in one go.
|}

'''''

'''(f)''' The '''Intrinisic Reaction Coordinate/IRC plots''' a series of points by taking small geometric steps follow the direction
in which the gradient is the steepest on the PE surface and this gives rise to the reaction path after the transition state.

'''''

Open optimized chair/boat transition structures -> Calculate: Gaussian -> Job Type: IRC; forward; once; 50 -> Submit.
Since the RMS gradient has not reached a minimum yet, the follwing methods are used in order further minimize it:
'''(1)''' Copy and paste structure 51 obtained in IRC to a new molgroup and run a normal minimization;
'''(2)''' Carry out IRC as the one above with number of points=200;
'''(3)''' Redo the IRC and choose force constants: always.

'''''

'''Results obtained by using three different methods above:'''

'''''

{| border="2"
|-
! '''Boat TS'''
! '''Method 1'''
! '''Method 2'''
! '''Method 3'''

|-
| '''Jmol of the final structure obtained'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>IRC_BOAT_METHOD1_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>IRC_BOAT_MIN2_100_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>boat_irc3jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| '''Result summary'''
| [[Image:IRC_BOAT_METHOD1_RS.jpg|center|thumb]]
| [[Image:IRC_BOAT_MIN2_RS_100.jpg|center|thumb]]
| [[Image:boat_irc_3_rs.jpg|center|thumb]]

|-
| '''IRC'''
| [[Image:IRG_BOAT1.jpg|center|thumb]]
| [[Image:IRC_BOAT_MIN2_RMS.jpg|center|thumb]]
| [[Image:boat_irc_3.jpg|center|thumb]]

|-
| '''Comment'''
| Min. E= -231.69266121 a.u.
Point group= C1
fastest/ end up in the wrong minimum if the starting structure is not close enough to a local minimum
| Min. E= -231.69194563 a.u.
Point group= C1
more reliable/ too many points may veer off in the wrong direction therefore end up wit the wrong minimum;
| Min. E= -231.69266113 a.u.
Point group= C1
the most reliable/ the most expensive and may not be feasible for large molecules.
|}

'''''

{| border="2"
|-
! '''Chair TS'''
! '''Method 1'''
! '''Method 2'''
! '''Method 3'''

|-
| '''Jmol of the final structure obtained'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>blue</color><size>150</size>
<uploadedFileContents>IRC_CHAIR_51JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>blue</color><size>150</size>
<uploadedFileContents>IRC_CHAIR_MIN2_100_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>blue</color><size>150</size>
<uploadedFileContents>chair_irc3jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| '''Result summary'''
| [[Image:IRC_CHAIR_METHOD1_RS.jpg|center|thumb]]
| [[Image:IRC_CHAIR_MIN2_RS_100.jpg|center|thumb]]
| [[Image:chair_irc_3_rs.jpg|center|thumb]]

|-
| '''IRC'''
| [[Image:IRC_CHAIR1.jpg|center|thumb]]
| [[Image:IRC_CHAIR_MIN_2_RMS.jpg|center|thumb]]
| [[Image:chair_irc_3.jpg|center|thumb]]

|-
| '''Comment'''
| Min. E= -231.69166698 a.u.
Point group= C2
fastest/ end up in the wrong minimum if the starting structure is not close enough to a local minimum
| Min. E= -231.69164474 a.u.
Point group= C2
more reliable/ too many points may veer off in the wrong direction therefore end up wit the wrong minimum;
| Min. E= -231.69166674 a.u.
Point group= C2
the most reliable/ the most expensive and may not be feasible for large molecules.
|}

'''''

'''Conclusion:''' By using different approaches, the symmetry obtained for each is the same, C1 for the '''Boat''' structure and C2 for the '''Chair''' structure; the '''Boat''' structure obtained matches well with Gauche 3 whereas the '''Chair''' structure matches well with the Gauche 2, this tells us the conformers involved in the cope rearrangement; the energy obtained for the '''Boat''' structure is always lower than that of the '''chair''' in regardless of the method used, which indicates the Boat structure is the thermodynamically preferred structure.

'''''

'''(g)'''Calculate the activation energies for the reaction via both transition structures:

start from the HF/3-21G optimized structures -> carry out opt+freq for both chair and boat transition structures using B3LYP/6-31G(d).

1 Hartree= 627.509 391 kcal/mol
therefore:

{| border="2"
|-
! /
! Jmol
! Results summary
! '''ΔE under B3LYP/6-31G(d) at 298.15K'''
! '''Experimental ΔE at 0K'''

|-
| '''Chair'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>blue</color><size>150</size>
<uploadedFileContents>chair_ts_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
| [[Image:yun_g_chair_ts_rs.jpg|center|thumb]]
| 33.69
| 33.5±0.5

|-
| '''Boat'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>boat_ts_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
| [[Image:yun_g_boat_ts_rs.jpg|center|thumb]]
| 42.23
| 44.7±2.0
|}

'''''

'''Conclusion:'''

The calculated activation energies match well with the experimental ones and the energy for each conformer obtained under the HF/3-21G and B3LYP/6-31G(d) methods are quite different in regardless of their similarity in geometry. Therefore, the higher level optimization could carried out based on the result obtained from the lower level of optimization in order to be more time efficient.

'''''

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T16:08:15Z

Yz1506:

==== '''Exercise: The Diels Alder Cycloaddition''' ====

'''''

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''''

'''The Diels-Alder reaction between ethylene and butadiene'''

'''''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap siginificantly, otherwise, the reaction is forbbidden.

'''''

'''Exercise'''

The AM1 semi-empirical molecular orbital method are used for these calculations at the beginning.

'''''

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

'''''

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

'''''

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

'''''

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| '''Symmetry w.r.t plane'''
| Asymmetric
| Symmetric
|}

'''''

The above procedures have been repeated for '''ethylene''':

'''''

{| border="2"
|-
! '''Jmol of ethylene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

'''''

Plot the '''HOMO''' and '''LUMO''' of '''ethylene''' and determine its symmetry:

'''''

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Ethylene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| '''Symmetry w.r.t plane'''
| Symmetric
| Asymmetric
|}

'''''

'''ii)''' Computate the '''Transition State geometry''' and examine the nature of the reaction path for the prototype reaction.

'''''

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.

The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

'''''

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

'''''

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

'''''

Plot the '''HOMO''' and '''LUMO''' of '''transition structure''' and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene.

'''''

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

'''''

The reaction is allowed in a concerted stereospecific fashion a result of the asymmetric HOMO of cis-butadiene overlaps with the asymmetric LUMO of ethylene; the symmetric LUMO of cis-butadiene overlaps with the symmetric LUMO of ethylene; these HOMO-LUMO pair interactions forms an asymmetric HOMO of the resulting adduct consisting of two new σ bonds.

'''''

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

'''''

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''''

Sketch the endo and exo products in Gaussview -> Calculate: Gaussian -> Job list: opt+freq; once -> Method: HF/3-21G -> Submit.
Then, beased on the optimized geometries, the two conformers are optimized futher at B3LYP/6-31G(d) level of theory.

'''''

'''Results for Endo and Exo products:'''

'''''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

'''''

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

'''''

From the results obtained above, the endo product is lower in energy than the exo one and therefore endo is more favoured, the reason for this is because when the dieneophile is substituted, the π orbitals in substituents can interact with the new double bond which forms in the product, this interaction stabilises the regiochemistry of the endo form more than that of the exo form(so-called the secondary orbital overlap effect), and this effect determines which transition state conformer is more favoured.

'''''

The optimisation was carried out by using the Hessian method based on a guessed transition structure(intermolecular bond length of the chain end carbons= 2.1A), but in order to get a reasonable guessed transition struture, both cyclohexa-1,3-diene and maleic anhydride were optimized first and then combined together to give the exo and endo transition structures.

'''''

'''Results for Endo and Exo tansition states:'''

'''''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

'''''

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''''

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

'''''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

'''''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

'''''

The typical sp3 and sp2 C-C bondlengths are 1.54Å and 1.34Å respectively, the double bond in cyclohexa-1,3-diene at the transition state is 1.397Å which is somewhere in between a double and single carbon carbon bond. The van der Waal radius of carbon is 1.702Å and the bond forming distances for the endo and exo transition states are 2.16Å, 2.17Å respectively, which indicates the orbitals do not overlap significantly and hence gives rise to a transition state in this case.

'''''

For the reaction of cyclohexa-1,3-diene with maleic anhydride, the exo product is more strained because the bridging group and the -C=O-CO-C=O- fragment are pointing in the same direction whereas in the endo product, they are pointing away from each other.
There is only one major nodal plane has been observed which is in between the HOMO between the -C=O-CO-C=O- fragment(x-axis, in this case).

'''''

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T16:07:23Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

==== '''Exercise: The Diels Alder Cycloaddition''' ====

'''''

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''''

'''The Diels-Alder reaction between ethylene and butadiene'''

'''''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap siginificantly, otherwise, the reaction is forbbidden.

'''''

'''Exercise'''

The AM1 semi-empirical molecular orbital method are used for these calculations at the beginning.

'''''

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

'''''

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

'''''

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

'''''

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| '''Symmetry w.r.t plane'''
| Asymmetric
| Symmetric
|}

'''''

The above procedures have been repeated for '''ethylene''':

'''''

{| border="2"
|-
! '''Jmol of ethylene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

'''''

Plot the '''HOMO''' and '''LUMO''' of '''ethylene''' and determine its symmetry:

'''''

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Ethylene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| '''Symmetry w.r.t plane'''
| Symmetric
| Asymmetric
|}

'''''

'''ii)''' Computate the '''Transition State geometry''' and examine the nature of the reaction path for the prototype reaction.

'''''

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.

The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

'''''

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

'''''

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

'''''

Plot the '''HOMO''' and '''LUMO''' of '''transition structure''' and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene.

'''''

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

'''''

The reaction is allowed in a concerted stereospecific fashion a result of the asymmetric HOMO of cis-butadiene overlaps with the asymmetric LUMO of ethylene; the symmetric LUMO of cis-butadiene overlaps with the symmetric LUMO of ethylene; these HOMO-LUMO pair interactions forms an asymmetric HOMO of the resulting adduct consisting of two new σ bonds.

'''''

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

'''''

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''''

Sketch the endo and exo products in Gaussview -> Calculate: Gaussian -> Job list: opt+freq; once -> Method: HF/3-21G -> Submit.
Then, beased on the optimized geometries, the two conformers are optimized futher at B3LYP/6-31G(d) level of theory.

'''''

'''Results for Endo and Exo products:'''

'''''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

'''''

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

'''''

From the results obtained above, the endo product is lower in energy than the exo one and therefore endo is more favoured, the reason for this is because when the dieneophile is substituted, the π orbitals in substituents can interact with the new double bond which forms in the product, this interaction stabilises the regiochemistry of the endo form more than that of the exo form(so-called the secondary orbital overlap effect), and this effect determines which transition state conformer is more favoured.

'''''

The optimisation was carried out by using the Hessian method based on a guessed transition structure(intermolecular bond length of the chain end carbons= 2.1A), but in order to get a reasonable guessed transition struture, both cyclohexa-1,3-diene and maleic anhydride were optimized first and then combined together to give the exo and endo transition structures.

'''''

'''Results for Endo and Exo tansition states:'''

'''''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

'''''

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''''

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

'''''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

'''''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

'''''

The typical sp3 and sp2 C-C bondlengths are 1.54Å and 1.34Å respectively, the double bond in cyclohexa-1,3-diene at the transition state is 1.397Å which is somewhere in between a double and single carbon carbon bond. The van der Waal radius of carbon is 1.702Å and the bond forming distances for the endo and exo transition states are 2.16Å, 2.17Å respectively, which indicates the orbitals do not overlap significantly and hence gives rise to a transition state in this case.

'''''

For the reaction of cyclohexa-1,3-diene with maleic anhydride, the exo product is more strained because the bridging group and the -C=O-CO-C=O- fragment are pointing in the same direction whereas in the endo product, they are pointing away from each other.
There is only one major nodal plane has been observed which is in between the HOMO between the -C=O-CO-C=O- fragment(x-axis, in this case).

'''''

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T16:00:12Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap siginificantly, otherwise, the reaction is forbbidden.

'''Exercise'''

The AM1 semi-empirical molecular orbital method are used for these calculations at the beginning.

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| '''Symmetry w.r.t plane'''
| Asymmetric
| Symmetric
|}

'''''

The above procedures have been repeated for '''ethylene''':

{| border="2"
|-
! '''Jmol of ethylene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the '''HOMO''' and '''LUMO''' of '''ethylene''' and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Ethylene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| '''Symmetry w.r.t plane'''
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the '''Transition State geometry''' and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the '''HOMO''' and '''LUMO''' of '''transition structure''' and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene.

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed in a concerted stereospecific fashion a result of the asymmetric HOMO of cis-butadiene overlaps with the asymmetric LUMO of ethylene; the symmetric LUMO of cis-butadiene overlaps with the symmetric LUMO of ethylene; these HOMO-LUMO pair interactions forms an asymmetric HOMO of the resulting adduct consisting of two new σ bonds.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

Sketch the endo and exo products in Gaussview -> Calculate: Gaussian -> Job list: opt+freq; once -> Method: HF/3-21G -> Submit.
Then, beased on the optimized geometries, the two conformers are optimized futher at B3LYP/6-31G(d) level of theory.

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

From the results obtained above, the endo product is lower in energy than the exo one and therefore endo is more favoured, the reason for this is because when the dieneophile is substituted, the π orbitals in substituents can interact with the new double bond which forms in the product, this interaction stabilises the regiochemistry of the endo form more than that of the exo form(so-called the secondary orbital overlap effect), and this effect determines which transition state conformer is more favoured.

The optimisation was carried out by using the Hessian method based on a guessed transition structure(intermolecular bond length of the chain end carbons= 2.1A), but in order to get a reasonable guessed transition struture, both cyclohexa-1,3-diene and maleic anhydride were optimized first and then combined together to give the exo and endo transition structures.

'''Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

The typical sp3 and sp2 C-C bondlengths are 1.54Å and 1.34Å respectively, the double bond in cyclohexa-1,3-diene at the transition state is 1.397Å which is somewhere in between a double and single carbon carbon bond. The van der Waal radius of carbon is 1.702Å and the bond forming distances for the endo and exo transition states are 2.16Å, 2.17Å respectively, which indicates the orbitals do not overlap significantly and hence gives rise to a transition state in this case.

For the reaction of cyclohexa-1,3-diene with maleic anhydride, the exo product is more strained because the bridging group and the -C=O-CO-C=O- fragment are pointing in the same direction whereas in the endo product, they are pointing away from each other.
There is only one major nodal plane has been observed which is in between the HOMO between the -C=O-CO-C=O- fragment(x-axis, in this case).

'''''

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T15:44:42Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The above procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of ethylene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Ethylene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene.

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed in a concerted stereospecific fashion a result of the asymmetric HOMO of cis-butadiene overlaps with the asymmetric LUMO of ethylene; the symmetric LUMO of cis-butadiene overlaps with the symmetric LUMO of ethylene; these HOMO-LUMO pair interactions forms an asymmetric HOMO of the resulting adduct consisting of two new σ bonds.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

From the results obtianed above, the endo product is lower in energy than the exo one and therefore endo is more favoured, the reason for this is because when the dieneophile is substituted, the π orbitals in substituents can interact with the new double bond which forms in the product, this interaction stabilises the regiochemistry the endo form more than that of the exo form(so-called the secondary orbital overlap effect), and this effect determines which transition state conformer is more favoured.

'''Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

The typical sp3 and sp2 C-C bondlengths are 1.54Å and 1.34Å respectively, the double bond in cyclohexa-1,3-diene at the transition state is 1.397Å which is somewhere in between a double and single carbon carbon bond. The van der Waal radius of carbon is 1.702Å and the bond forming distances for the endo and exo transition states are 2.16Å, 2.17Å respectively, which indicates the orbitals do not overlap significantly and hence gives rise to a transition state in this case.

For the reaction of cyclohexa-1,3-diene with maleic anhydride, the exo product is more strained because the bridging group and the -C=O-CO-C=O- fragment are pointing in the same direction whereas in the endo product, they are pointing away from each other.
There is only one major nodal plane has been observed which is in between the HOMO between the -C=O-CO-C=O- fragment(x-axis, in this case).

'''''

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T15:44:04Z

Yz1506:

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The above procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of ethylene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Ethylene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene.

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed in a concerted stereospecific fashion a result of the asymmetric HOMO of cis-butadiene overlaps with the asymmetric LUMO of ethylene; the symmetric LUMO of cis-butadiene overlaps with the symmetric LUMO of ethylene; these HOMO-LUMO pair interactions forms an asymmetric HOMO of the resulting adduct consisting of two new σ bonds.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

From the results obtianed above, the endo product is lower in energy than the exo one and therefore endo is more favoured, the reason for this is because when the dieneophile is substituted, the π orbitals in substituents can interact with the new double bond which forms in the product, this interaction stabilises the regiochemistry the endo form more than that of the exo form(so-called the secondary orbital overlap effect), and this effect determines which transition state conformer is more favoured.

'''Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

The typical sp3 and sp2 C-C bondlengths are 1.54Å and 1.34Å respectively, the double bond in cyclohexa-1,3-diene at the transition state is 1.397Å which is somewhere in between a double and single carbon carbon bond. The van der Waal radius of carbon is 1.702Å and the bond forming distances for the endo and exo transition states are 2.16Å, 2.17Å respectively, which indicates the orbitals do not overlap significantly and hence gives rise to a transition state in this case.

For the reaction of cyclohexa-1,3-diene with maleic anhydride, the exo product is more strained because the bridging group and the -C=O-CO-C=O- fragment are pointing in the same direction whereas in the endo product, they are pointing away from each other.
There is only one major nodal plane has been observed which is in between the HOMO between the -C=O-CO-C=O- fragment(x-axis, in this case).

'''''

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T15:27:16Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The above procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of ethylene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Ethylene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene.

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed in a concerted stereospecific fashion a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

From the results obtianed above, the endo product is lower in energy than the exo one and therefore endo is more favoured, the reason for this is because the endo form has more secondary orbital overlap effect, therefore more stablized than the exo form.

'''Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

The typical sp3 and sp2 C-C bondlengths are 1.54Å and 1.34Å respectively, the double bond in cyclohexa-1,3-diene at the transition state is 1.397Å which is somewhere in between a double and single carbon carbon bond. The van der Waal radius of carbon is 1.702Å and the bond forming distances for the endo and exo transition states are 2.16Å, 2.17Å respectively, which indicates the orbitals do not overlap significantly and hence gives rise to a transition state in this case.

For the reaction of cyclohexa-1,3-diene with maleic anhydride, the exo product is more strained because the bridging group and the -C=O-CO-C=O- fragment are pointing in the same direction whereas in the endo product, they are pointing away from each other.
There is only one major nodal plane has been observed which is in between the HOMO between the -C=O-CO-C=O- fragment(x-axis, in this case).

'''''

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T15:03:21Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of ethylene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Ethylene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene.

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed in a concerted stereospecific fashiona a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

The transition structure was then calculated at the HF/3-21G level of theory using the Berny TS in the optimisation. The initial bond forming distances were defined as 2.2 Å and the calculation was sucessful. The optimised TS structure had an energy E=-231.60320844 Hartree and bond forming distances of 2.2102 Å and 2.20854 Å and the TS was confirmed by an imaginery frequency at -818.777 cm-1, that correlates to the Diels-Alder. The HOMO orbital of the TS structrue was then visualised from the check point file and this can be seen below:

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

From the results obtianed above, the endo product is lower in energy than the exo one and therefore endo is more favoured, the reason for this is because the endo form has more secondary orbital overlap effect, therefore more stablized than the exo form.

'''Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

* What can you conclude about the so called “secondary orbital overlap effect”?
Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

* What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

* Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

The formaion of the two bonds are synchronous and .......

For the cyclohexa-1,3-diene reaction with maleic anhydride:
the exo form is more strained because the bridging and the -C=O-CO-C=O- fragment are pointing in the same direction whereas in the endo form, they are pointing in opposite direction.
Only one major nodal plane has been observed in the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system.

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Physical

2009-02-27T12:44:16Z

Yz1506: New page: =='''Module3, Experiment 3: The Transition State'''== In this experiment, the transition state structures in larger molecules for Cope rearrangement and Diels Alder cycloaddition reaction...

=='''Module3, Experiment 3: The Transition State'''==

In this experiment, the transition state structures in larger molecules for Cope rearrangement and Diels Alder cycloaddition reactions are studies using molecular orbital-based computaional methods which solve the Schrodinger equation numerically and locate the transition state structures based on the local shape of a potential energy surface. It also gives us information about the shapes of the transition structures, the pathways in which the reaction undergoes and how big the barrier heights are.

'''''

===''The Cope Rearrangement Tutorial'' ===

'''Chemical reactivity of the Cope rearrangement of 1,5-hexadiene'''

'''Objectives:'''

locate the low-energy minima and transition structures on the C6H10 potential energy surface and determine the preferred reaction mechanism.

The [3,3]-sigmatropic shift rearrangement occurs in a concerted fashion(6 electrons; 4n+2; heat)via either a "chair" or a "boat" transition structure, with the "boat" transition structure lying several kcal/mol higher in energy. The B3LYP/6-31G* optimisation was carried by using Gaussian and see how it matchees with this result.

'''''

{| border="2"
|-
! '''Cope rearrangement'''
! '''Chair Transition State'''
! '''Boat Transition State'''
|-
|[[Image:Cope rearrangement.jpg|center|Cope rearrangement ]]
|[[Image:Chair Transition State1 .jpg|center|Chair Transition State ]]
|[[Image:Boat Transition State .jpg|center|Boat Transition State ]]
|}

'''''

==== '''Optimizing the Reactants and Products''' ====

'''(a)''' Open GaussView -> in the '''Molecule''' window: draw 1,5-hexadiene with an "anti" linkage for the central four C atoms -> click "Clean" under the "Edit" menu.
"Calculate" -> "Gaussian" -> "Job type": optimization -> "Method": Hartree-Fock -> "Basis set": 3-21G -> "Link 0": %mem=250MB -> Submit -> save as "yun_react_anti" -> after job has finished, open the file -> Select "Yes" -> Files of type: choose *.chk -> Open "yun_react_anti" in the C:\Windows\G03\Scratch folder -> "Result": Summary -> "Edit": Symmetrize.

'''''

{| border="2"
|-
! '''1,5-hexadiene with an "anti" linkage
for the central four C atoms'''
! '''Results Summary'''
|-
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>1,5-hexadiene with an anti linkage.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:anti3_rs.jpg|center|]]
|}

The structure is the same one as '''Anti 3''' in Appendix 1

'''''

'''(b)''' Draw 1,5-hexadiene with a "gauche" linkage for the central four C atoms and optimize the structure at the HF/3-21G level of theory.

Would you expect this structure to have a lower or a higher energy than the anti structure you have just optimized?

Both gauche and anti conformers are very similar in enenrgy; if the electrostatic effect(eg. gauche
effect) overweighs the steric effect, the gauche conformers are preferred and vice versa.

'''''

{| border="2"
|-
! '''1,5-hexadiene with a "gauche" linkage
for the central four C atoms'''
! '''Results Summary'''
|-
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>green</color><size>150</size>
<uploadedFileContents>yun_react_gau4jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:gauche4_rs.jpg|center|]]
|}

The structure is the same one as '''Gauche 4''' in Appendix 1

'''''

'''(c)-(e)''' Based on the results above, predict the lowest energy conformation of 1,5-hexadiene and test out your hypothesis by drawing the structure and optimizing it.

The gauche conformer for 1,5-hexadiene is more stable than that of the anti conformer from thre optimisation above; in the hypothesis test, all the gauche and anti conformers have been optimised at HF/3-21G level of theory.
The names of the structure optimized are given by the matching structure in [Appendix 1].
Hypothesis test:

{| border="2"
|-
! '''Gauche conformer'''
! '''Jmol'''
! '''Results Summary'''
|-
|'''Gauche1'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>green</color><size>150</size>
<uploadedFileContents>gauche1jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:gauch1_rs.jpg|center|]]

|-
|'''Gauche2'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>green</color><size>150</size>
<uploadedFileContents>gauche2jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:gauch2_rs.jpg|center|]]

|-
|'''Gauche3'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>green</color><size>150</size>
<uploadedFileContents>gauche3jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:gauch3_rs.jpg|center|]]

|-
|'''Gauche5'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>green</color><size>150</size>
<uploadedFileContents>gauche5jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:gauch5_rs.jpg|center|]]

|-
|'''Gauche6'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>green</color><size>150</size>
<uploadedFileContents>gauche6jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:gauche6_rs.jpg|center|]]
|}

'''''

{| border="2"
|-
! '''Anti conformer'''
! '''Jmol'''
! '''Results Summary'''
|-
|'''Anti1'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>anti1jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:anti1_rs.jpg|center|]]

|-
|'''Anti2'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>anti2jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:anti2_rs.jpg|center|]]

|-
|'''Anti4'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>anti4jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:anti4_rs.jpg|center|]]
|}

The energy obtained for each conformer is well matched with the ones shown in [Appendix 1] which conforms the optimisation has been carried out correctly.

'''''

'''(f)''' The structures are reoptimized at the B3LYP/6-31G(d)level:

{| border="2"
|-
! '''Gauche conformer'''
! '''Jmol'''
! '''Results Summary'''

|-
|'''Gauche1'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>gau1jmol_DFT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:gau1_rs_DFT.jpg|center|]]

|-
|'''Gauche2'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>gau2jmol_DFT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:gau2_rs_DFT.jpg|center|]]

|-
|'''Gauche3'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>gau3jmol_DFT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:gau3_rs_DFT.jpg|center|]]

|-
|'''Gauche4'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>gau4jmol_DFT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:gau4_rs_DFT.jpg|center|]]

|-
|'''Gauche5'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>gau5jmol_DFT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:gau5_rs_DFT.jpg|center|]]

|-
|'''Gauche6'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>gau6jmol_DFT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:gau6_rs_DFT.jpg|center|]]
|}

'''''

{| border="2"
|-
! '''Anti conformer'''
! '''Jmol'''
! '''Results Summary'''
|-
|'''Anti1'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>yellow</color><size>150</size>
<uploadedFileContents>anti1jmol_DFT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:anti1_rs_DFT.jpg|center|]]

|-
|'''Anti2'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>yellow</color><size>150</size>
<uploadedFileContents>anti2jmol_DFT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:anti2_rs_DFT.jpg|center|]]

|-
|'''Anti3'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>yellow</color><size>150</size>
<uploadedFileContents>anti3jmol_DFT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:anti3_rs_DFT.jpg|center|]]

|-
|'''Anti4'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>yellow</color><size>150</size>
<uploadedFileContents>anti4jmol_DFT.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:anti4_rs_DFT.jpg|center|]]
|}

'''''

Compare the final structures from the HF/3-21G calculation with that at the higher level of theory. How much does the overall geometry change?

There is no significant change in geometry and all the point group stays the same for for all the conformers when a higher level of optimization is carried out. However the energy is minimized further when the B3LYP/6-31G(d) level of theory is applied.
Geometric information under B3LYP/6-31G and B3LYP/6-31G(d) methods:

{| border="2"
|-
! /
! '''Structure obtained under HF/3-21G optimisation'''
! '''Bond length/angle obtained under HF/3-21G optimisation'''
! '''Structure obtained under DFT/B3LYPT(d)optimisation'''
! '''Bond length/angle obtained under DFT/B3LYPT(d)optimisation'''

|-
| '''Gauche1'''
|[[Image:gau1_st.jpg|center|]]
|[[Image:gau1_al.jpg|center|thumb]]
|[[Image:gau1_st_DFT.jpg|center|]]
|[[Image:gau1_al_DFT.jpg|center|thumb]]

|-
| '''Gauche2'''
|[[Image:gau2_st.jpg|center|]]
|[[Image:gau2_al.jpg|center|thumb]]
|[[Image:gau2_st_DFT.jpg|center|]]
|[[Image:gau2_al_DFT.jpg|center|thumb]]

|-
| '''Gauche3'''
|[[Image:gau3_st.jpg|center|]]
|[[Image:gau3_al.jpg|center|thumb]]
|[[Image:gau3_st_DFT.jpg|center|]]
|[[Image:gau3_al_DFT.jpg|center|thumb]]

|-
| '''Gauche4'''
|[[Image:gau4_st.jpg|center|]]
|[[Image:gau4_al.jpg|center|thumb]]
|[[Image:gau4_st_DFT.jpg|center|]]
|[[Image:gau4_al_DFT.jpg|center|thumb]]

|-
| '''Gauche5'''
|[[Image:gau5_st.jpg|center|]]
|[[Image:gau5_al.jpg|center|thumb]]
|[[Image:gau5_st_DFT.jpg|center|]]
|[[Image:gau5_al_DFT.jpg|center|thumb]]

|-
| '''Gauche6'''
|[[Image:gau6_st.jpg|center|]]
|[[Image:gau6_al.jpg|center|thumb]]
|[[Image:gau6_st_DFT.jpg|center|]]
|[[Image:gau6_al_DFT.jpg|center|thumb]]

|-
| '''Anti1'''
|[[Image:anti1_st.jpg|center|]]
|[[Image:anti1_al.jpg|center|thumb]]
|[[Image:anti1_st_DFT.jpg|center|]]
|[[Image:anti1_al_DFT.jpg|center|thumb]]

|-
| '''Anti2'''
|[[Image:anti2_st.jpg|center|]]
|[[Image:anti2_al.jpg|center|thumb]]
|[[Image:anti2_st_DFT.jpg|center|]]
|[[Image:anti2_al_DFT.jpg|center|thumb]]

|-
| '''Anti3'''
|[[Image:anti3_st.jpg|center|]]
|[[Image:anti3_al.jpg|center|thumb]]
|[[Image:anti3_st_DFT.jpg|center|]]
|[[Image:anti3_al_DFT.jpg|center|thumb]]

|-
| '''Anti4'''
|[[Image:anti4_st.jpg|center|]]
|[[Image:anti4_al.jpg|center|thumb]]
|[[Image:anti4_st_DFT.jpg|center|]]
|[[Image:anti4_al_DFT.jpg|center|thumb]]
|}

'''''

'''(g)''' Open the optimized B3LYP/6-31G(d) structure -> Calculate: Gussian -> Job type: Frequency -> Method: DFT； B3LYP/6-31G（d) -> link 0: yun_freq_gau1_DFT.chk -> save -> run -> Once the job has finished, open yun_freq_gau1_DFT.log -> Results menu: Vibrations -> Check there are only real frequencies -> Spectrum.

There is no imaginary vibrational frequencies for all the structures as shown in the B3LYP/6-31G(d) result summary table, this means that a minimum energy is obtained for all the structures.

On '''Results''' menu: View File -> find Thermochemistry -> find Vibrational temperatures: a list of energies -> Make a note of
'''(i) the sum of electronic and zero-point energies(E = Eelec + ZPE); (ii) the sum of electronic and thermal energies(E = E + Evib + Erot + Etrans); (iii) the sum of electronic and thermal enthalpies(H = E + RT); (iv) the sum of electronic and thermal free energies(G = H - TS).'''

Results:

{| border="2"
|-
! '''Name of structure'''
! '''Energy data'''

|-
| '''Gauche1'''
|[[Image:gau1_E.jpg|center|]]

|-
| '''Gauche2'''
|[[Image:gau2_E.jpg|center|]]

|-
| '''Gauche3'''
|[[Image:gau3_E.jpg|center|]]

|-
| '''Gauche4'''
|[[Image:gau4_E.jpg|center|]]

|-
| '''Gauche5'''
|[[Image:gau5_E.jpg|center|]]

|-
| '''Gauche6'''
|[[Image:gau6_E.jpg|center|]]

|-
| '''Anti1'''
|[[Image:anti1_E.jpg|center|]]

|-
| '''Anti2'''
|[[Image:anti2_E.jpg|center|]]

|-
| '''Anti3'''
|[[Image:anti3_E.jpg|center|]]

|-
| '''Anti4'''
|[[Image:anti4_E.jpg|center|]]
|}

'''''

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

'''''

''' Optimizing the "Chair" Transition Structures'''

'''''

'''(a)''' Draw a planar allyl fragment(CH2CHCH2)-> run a HF/3-21G level optimisation -> copy this structure to a new GaussView window
twice and orient for them to look like the '''chair''' transition state (translate one fragment: Shift Alt keys + Left Mouse button;
rotate: Alt key + Left)-> Bond distance between the terminal Cs of the CH2CHCH2 fragments ~ 2.2 Å -> Save as chair_ts_guess.

'''''

'''(b)''' Use Hartree Fock and the default basis set 3-21G for parts (b) to (f).
'''Optimization by using Hessian:'''
File → New → Create MolGroup -> copy and paste the guess structure into the window -> Calculation: Gaussian -> Job Type:
Opt+Freq; Optimization to a: TS (Berny); calculate force constants: Once; Additional keyword: Opt=NoEigen -> Submit.
After the job completes, it gives an imaginary frequency '''-817.897cm-1''' due to the Cope rearrangement.

'''''

'''Optimization by using Frozen coordinate:'''
'''(c)''' Frozen coordinate optimization: File → New → Create MolGroup -> copy and paste the guess structure into the window ->
Edit: Redundant Coord Editor -> click on Create a New Coordinate -> On GaussView window: select 2 of the terminal Cs from the
CH2CHCH2 fragments which form/break a bond during the rearrangement -> On coordinate editor: select Coordination: Bond; Freeze
Coordinate -> Set value: 2.2 -> click on Create a New Coordinate -> select the opposite 2 terminal Cs -> select Bond and Freeze
Coordinate -> Click OK -> Submit.
'''(d)''' Open the file after the job has finished -> Edit: Redundant Coord Editor -> create a new coordinate by clicking on Create
a New Coordinate -> Select one of the bonds that was frozen before -> Coordinative: Bond; Derivative -> Repeat this procedure for
the other bond -> Calculate: Gaussian -> Job type: opt+freq; optimize to a: TS(Berny); Calulate Force Constants: Never ->
yun_opt_freq_redundant2 -> submit. This transition structure gives an imaginary frequency '''-817.947cm-1''' due to the Cope rearrangement.

'''''

'''Results:'''

{| border="2"
|-
! /
! '''Chair transition structure(Optimized under Hessian)'''
! '''Chair transition structure(Optimized under Redundant)'''

|-
| '''Jmol'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>blue</color><size>150</size>
<uploadedFileContents>chair_HF_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>blue</color><size>150</size>
<uploadedFileContents>RD_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| '''Result summary'''
| [[Image:chair_HF_rs.jpg|center|thumb]]
| [[Image:chair_RD_rs.jpg|center|thumb]]
|-
| '''Imaginary frequency'''
| [[Image:IM_HF.jpg|center|thumb]]
| [[Image:IM_RD.jpg|center|thumb]]
|-
| '''Geometric information(atom list)'''
| [[Image:HF_AL_CHAIR.jpg|center|thumb]]
| [[Image:RD_AL_CHAIR.jpg|center|thumb]]
|}

'''''

''' Optimizing the "Boat" Transition Structures'''

'''(e) Optimization by using the QST2 method''':
Open the chk file of anti2 -> open a second window -> create a new MolGroup -> copy anti2 molecule into the new window
and select File → New → Add to MolGroup(the original molecule disappears and a green circle appearwith a 2 next to
it -> copy and paste the reactant molecule again and we are going to make it the product molecule -> click on the
icon showing two molecules side by side -> View: select Labels and change the numbering.
'''Set up the 1st QST2 optimization:'''
On '''Gaussian''' menu -> Job Type: Opt+Freq; optimize to a: TS (QST2)-> Submit -> job fails.

{| border="2"
|-
! [[Image:fail.jpg|center|thumb]]
! [[Image:Fail_chair.jpg|center|thumb]]
! The structure looks like chair transition state but with bonds more dissociated, this is because the calculation translated the top CH3CH2CH3 fragment but did not rotate it around the central bonds.
|}

'''''

{| border="2"
|-
!'''Set up your QST2 calculation again''' by going back to the original input file and this time
modify the geometries of both molecules, for the reactant, make the central C-C-C-C dihedral angle 0
and the inside C-C-C angle 100. Repeat for the product molecule.
![[Image:sm_pd.jpg|left|thumb]]
|}

The '''QST2 calculation''' was then carried out.

'''Results:'''

{| border="2"
|-
! '''Jmol of the boat transition state under QST2 method'''
! '''Result summary'''
! '''Imaginary vibration'''
! '''Advantage and disadvantage of using the QST2 method'''

|-
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>QST2_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
| [[Image:QST2_RS.jpg|center|thumb]]
| [[Image:QST2_VB.jpg|center|thumb]]
| The QST2 method is easy to set up because it is fully automated, however the job has failed for serveal times before the correct optimisation was obtained due to the input guess transition structure is not close enough to the real one.
|}

'''''

'''Optimization by using the QST3 method''':

'''Result:'''

{| border="2"
|-
! '''Input image'''
! '''Result Summary and Imaginary vibration'''
! '''Advantage of using the QST3 method'''
|-
| [[Image:boat_2_freq_opt_QST3_importimage.jpg|center|thumb]]
| [[Image:boat_2_freq_opt_QST3_all.jpg|center|thumb]]
| The QST3 method is more reliable and the optimization is successfully carried out in one go.
|}

'''''

'''(f)''' The '''Intrinisic Reaction Coordinate/IRC plots''' a series of points by taking small geometric steps follow the direction
in which the gradient is the steepest on the PE surface and this gives rise to the reaction path after the transition state.

Open optimized chair/boat transition structures -> Calculate: Gaussian -> Job Type: IRC; forward; once; 50 -> Submit.
Since the RMS gradient has not reached a minimum yet, the follwing methods are used in order further minimize it:
'''(1)''' Copy and paste structure 51 obtained in IRC to a new molgroup and run a normal minimization;
'''(2)''' Carry out IRC as the one above with number of points=200;
'''(3)''' Redo the IRC and choose force constants: always.

'''Results obtained by using three different methods above:'''

{| border="2"
|-
! '''Boat TS'''
! '''Method 1'''
! '''Method 2'''
! '''Method 3'''

|-
| '''Jmol of the final structure obtained'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>IRC_BOAT_METHOD1_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>IRC_BOAT_MIN2_100_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>boat_irc3jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| '''Result summary'''
| [[Image:IRC_BOAT_METHOD1_RS.jpg|center|thumb]]
| [[Image:IRC_BOAT_MIN2_RS_100.jpg|center|thumb]]
| [[Image:boat_irc_3_rs.jpg|center|thumb]]

|-
| '''IRC'''
| [[Image:IRG_BOAT1.jpg|center|thumb]]
| [[Image:IRC_BOAT_MIN2_RMS.jpg|center|thumb]]
| [[Image:boat_irc_3.jpg|center|thumb]]

|-
| '''Comment'''
| Min. E= -231.69266121 a.u.
Point group= C1
fastest/ end up in the wrong minimum if the starting structure is not close enough to a local minimum
| Min. E= -231.69194563 a.u.
Point group= C1
more reliable/ too many points may veer off in the wrong direction therefore end up wit the wrong minimum;
| Min. E= -231.69266113 a.u.
Point group= C1
the most reliable/ the most expensive and may not be feasible for large molecules.
|}

'''''

{| border="2"
|-
! '''Chair TS'''
! '''Method 1'''
! '''Method 2'''
! '''Method 3'''

|-
| '''Jmol of the final structure obtained'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>blue</color><size>150</size>
<uploadedFileContents>IRC_CHAIR_51JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>blue</color><size>150</size>
<uploadedFileContents>IRC_CHAIR_MIN2_100_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>blue</color><size>150</size>
<uploadedFileContents>chair_irc3jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>

|-
| '''Result summary'''
| [[Image:IRC_CHAIR_METHOD1_RS.jpg|center|thumb]]
| [[Image:IRC_CHAIR_MIN2_RS_100.jpg|center|thumb]]
| [[Image:chair_irc_3_rs.jpg|center|thumb]]

|-
| '''IRC'''
| [[Image:IRC_CHAIR1.jpg|center|thumb]]
| [[Image:IRC_CHAIR_MIN_2_RMS.jpg|center|thumb]]
| [[Image:chair_irc_3.jpg|center|thumb]]

|-
| '''Comment'''
| Min. E= -231.69166698 a.u.
Point group= C2
fastest/ end up in the wrong minimum if the starting structure is not close enough to a local minimum
| Min. E= -231.69164474 a.u.
Point group= C2
more reliable/ too many points may veer off in the wrong direction therefore end up wit the wrong minimum;
| Min. E= -231.69166674 a.u.
Point group= C2
the most reliable/ the most expensive and may not be feasible for large molecules.
|}

'''''

'''Conclusion:''' By using different approaches, the symmetry obtained for each is the same, C1 for the '''Boat''' structure and C2 for the '''Chair''' structure; the '''Boat''' structure obtained matches well with Gauche 3 whereas the '''Chair''' structure matches well with the Gauche 2, this tells us the conformers involved in the cope rearrangement; the energy obtained for the '''Boat''' structure is always lower than that of the '''chair''' in regardless of the method used, which indicates the Boat structure is the thermodynamically preferred structure.

'''''

'''(g)'''Calculate the activation energies for the reaction via both transition structures:

start from the HF/3-21G optimized structures -> carry out opt+freq for both chair and boat transition structures using B3LYP/6-31G(d).

1 Hartree= 627.509 391 kcal/mol
therefore:

{| border="2"
|-
! /
! Jmol
! Results summary
! '''ΔE under B3LYP/6-31G(d) at 298.15K'''
! '''Experimental ΔE at 0K'''

|-
| '''Chair'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>blue</color><size>150</size>
<uploadedFileContents>chair_ts_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
| [[Image:yun_g_chair_ts_rs.jpg|center|thumb]]
| 33.69
| 33.5±0.5

|-
| '''Boat'''
|<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>purple</color><size>150</size>
<uploadedFileContents>boat_ts_jmol.mol</uploadedFileContents>
</jmolApplet>
</jmol>
| [[Image:yun_g_boat_ts_rs.jpg|center|thumb]]
| 42.23
| 44.7±2.0
|}

'''Conclusion:'''

The calculated activation energies match well with the experimental ones and the energy for each conformer obtained under the HF/3-21G and B3LYP/6-31G(d) methods are quite different in regardless of their similarity in geometry. Therefore, the higher level optimization could carried out based on the result obtained from the lower level of optimization in order to be more time efficient.

'''''

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of ethylene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Ethylene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

'''Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

* What can you conclude about the so called “secondary orbital overlap effect”?
Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

* What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

* Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

The formaion of the two bonds are synchronous and .......

For the cyclohexa-1,3-diene reaction with maleic anhydride:
the exo form is more strained because the bridging and the -C=O-CO-C=O- fragment are pointing in the same direction whereas in the endo form, they are pointing in opposite direction.
Only one major nodal plane has been observed in the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system.

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T12:39:19Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of ethylene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Ethylene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

'''Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

* What can you conclude about the so called “secondary orbital overlap effect”?
Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

* What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

* Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

The formaion of the two bonds are synchronous and .......

For the cyclohexa-1,3-diene reaction with maleic anhydride:
the exo form is more strained because the bridging and the -C=O-CO-C=O- fragment are pointing in the same direction whereas in the endo form, they are pointing in opposite direction.
Only one major nodal plane has been observed in the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system.

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T12:38:21Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of ethylene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Ethylene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

'''Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

* What can you conclude about the so called “secondary orbital overlap effect”?
Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

* What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

* Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

The formaion of the two bonds are synchronous and .......

For the cyclohexa-1,3-diene reaction with maleic anhydride:
the exo form is more strained because the bridging and the -C=O-CO-C=O- fragment are pointing in the same direction whereas in the endo form, they are pointing in opposite direction.
Only one major nodal plane has been observed in the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system.

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T12:20:34Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of ethylene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Ethylene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

'''Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T11:10:14Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

'''Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|]]
E= -0.020 a.u.
|}

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T11:09:33Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

'''Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exots_al.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|thumb]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|thumb]]
E= -0.020 a.u.
|}

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|thumb]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|thumb]]
E= -0.020 a.u.
|}

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T11:07:54Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}

'''Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

'''Results for the HOMO/LUMO for the Exo and Endo Transition state:'''

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Endo
|[[Image:endotslumo_0.028.jpg|center|thumb]]
E= 0.028 a.u.
|[[Image:endotslumo_-0.02.jpg|center|thumb]]
E= -0.020 a.u.
|}

{| border="2"
|-
! /
! '''HOMO'''
! '''LUMO'''
|-
| Exo
|[[Image:exotslumo_0.033.jpg|center|thumb]]
E= 0.033 a.u.
|[[Image:exotshomo_-0.02.jpg|center|thumb]]
E= -0.020 a.u.
|}

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

File:EXO TS JMOL.mol

2009-02-27T11:01:31Z

Yz1506:

File:EXO PD 631GD JMOL.mol

2009-02-27T11:01:21Z

Yz1506:

File:ENDO TS JMOL.mol

2009-02-27T11:01:12Z

Yz1506:

File:ENDO OPT 631GD JMOL.mol

2009-02-27T11:01:04Z

Yz1506:

File:Exotsvb.jpg

2009-02-27T11:00:47Z

Yz1506:

File:Exotshomo -0.02.jpg

2009-02-27T11:00:38Z

Yz1506:

File:Exots al.jpg

2009-02-27T11:00:38Z

Yz1506:

File:Exopd631 al.jpg

2009-02-27T11:00:00Z

Yz1506:

File:Exopd321 al.jpg

2009-02-27T10:59:37Z

Yz1506:

File:Endotslumo -0.02.jpg

2009-02-27T10:59:14Z

Yz1506:

File:Endots rs.jpg

2009-02-27T10:59:05Z

Yz1506:

File:Endopd631 rs.jpg

2009-02-27T10:58:56Z

Yz1506:

File:Endopd321 rs.jpg

2009-02-27T10:58:47Z

Yz1506:

File:Exotslumo 0.033.jpg

2009-02-27T10:58:32Z

Yz1506:

File:Exots rs.jpg

2009-02-27T10:58:14Z

Yz1506:

File:Exopd631 rs.jpg

2009-02-27T10:58:05Z

Yz1506:

File:Exopd321 rs.jpg

2009-02-27T10:57:55Z

Yz1506:

File:Endotsvb -805.614.jpg

2009-02-27T10:57:38Z

Yz1506:

File:Endots al.jpg

2009-02-27T10:57:27Z

Yz1506:

File:Endotslumo 0.028.jpg

2009-02-27T10:57:27Z

Yz1506:

File:Endopd631 al.jpg

2009-02-27T10:57:09Z

Yz1506:

File:Endopd321 al.jpg

2009-02-27T10:56:43Z

Yz1506:

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T10:56:06Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}
'''
Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_TS_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T10:53:50Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:endopd631_rs.jpg|center|thumb]]
|[[Image:endopd321_al.jpg|center|thumb]]
|[[Image:endopd631_al.jpg|center|thumb]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|thumb]]
|[[Image:exopd631_rs.jpg|center|thumb]]
|[[Image:exopd321_al.jpg|center|thumb]]
|[[Image:exopd631_al.jpg|center|thumb]]
|}
'''
Results for Endo and Exo tansition states:'''

{| border="2"
|-
! '''Jmol of Endo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endots_rs.jpg|center|thumb]]
|[[Image:endots_al.jpg|center|thumb]]
|[[Image:endotsvb_-805.614.jpg|center|thumb]]
-805.614cm-1
|}

{| border="2"
|-
! '''Jmol of Exo transition state'''
! '''Results summary'''
! '''Geometric information'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|thumb]]
|[[Image:exots_rs.jpg|center|thumb]]
|[[Image:exotsvb.jpg|center|thumb]]
-811.515cm-1
|}

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T10:48:21Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

'''Results for Endo and Exo products:'''

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:endopd321_rs.jpg|center|]]
|[[Image:endopd631_rs.jpg|center|]]
|[[Image:endopd321_al.jpg|center|]]
|[[Image:endopd631_al.jpg|center|]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(HF/3-21G)'''
! '''Geometric information(B3LYP/6-31G(d))'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:exopd321_rs.jpg|center|]]
|[[Image:exopd631_rs.jpg|center|]]
|[[Image:exopd321_al.jpg|center|]]
|[[Image:exopd631_al.jpg|center|]]
|}

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T10:16:26Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(Atom list)'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ENDO_OPT_321G_RS.jpg|center|]]
|[[Image:ENDO_OPT_631GD_RS.jpg|center|]]
|[[Image:endo_pd_al.jpg|center|]]
|}

{| border="2"
|-
! '''Jmol of Exo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(Atom list)'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>EXO_PD_321G_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:EXO_PD_321G_RS.jpg|center|]]
|[[Image:EXO_RD_631GD_RS.jpg|center|]]
|[[Image:exo_pd_al.jpg|center|]]
|}

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T10:13:52Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

{| border="2"
|-
! '''Jmol of Endo product'''
! '''Results summary under HF/3-21G'''
! '''Results summary under B3LYP/6-31G(d)'''
! '''Geometric information(Atom list)'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ENDO_OPT_631GD_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ENDO_OPT_321G_RS.jpg|center|]]
|[[Image:ENDO_OPT_631GD_RS.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T10:06:54Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)''' Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

As the reaction is controlled kinetically, the cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give the endo adduct(transition state energy).

Locate the transition structures for both 3 and 4. Compare the energies of the endo and exo forms.

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T10:04:25Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

The reaction is allowed as a result of the asymmetric HOMO of cis-butadiene and the asymmetric LUMO of ethylene overlap to give a asymmetric transition state structure.

'''(iii)'''Study the regioselectivity of the Diels Alder Reaction between cyclohexa-1,3-diene and maleic anhydride.

Cyclohexa-1,3-diene undergoes facile reaction with maleic anhydride to give primarily the endo adduct. The reaction is supposed to be kinetically controlled so that the exo transition state should be higher in energy.

Locate the transition structures for both 3 and 4. Compare the energies of the endo and exo forms.

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

Rep:Mod:Yunzhang Module3 Writeup3

2009-02-27T09:51:44Z

Yz1506: /* '''Exercise: The Diels Alder Cycloaddition''' */

If the dieneophile is substituted, with substituents that have π orbitals that can interact with the new double bond that is being formed in the product, then this interaction can stabilise the regiochemistry (i.e. head to tail versus tail to head) of the reaction. In this exercise you will study the nature of the transition structure for the Diels Alder reaction, both for the prototypical reaction and for the case where both diene and dieneophile carry substituents, and where secondary orbital effects are possible. Clearly, the factors that control the nature of the transition state are quantum mechanical in origin and thus we shall use methods based upon quantum chemistry.

The HOMO of ethylene and the LUMO of butadiene are both s (symmetric with respect to the reflection plane) and the LUMO of ethylene and the HOMO of butadiene are both a. Thus it is the HOMO-LUMO pairs of orbital that interact, and energetically, the HOMO of the resulting adduct with two new σ bonds is a.

==== '''Exercise: The Diels Alder Cycloaddition''' ====

In the Diels Alder reactions(6п electrons; Hueckel transition state; suprafacial ; heat), the dieneophile π orbitals is involved in forming a new σ bonds with the diene π orbitals. Depends on the number of π electrons involved in this process, the reaction happens in either allowed or forbidden stereospecific fashion.

'''The Diels-Alder reaction between ethylene and butadiene'''

In this exercise, the HOMO/LUMO of cis-butadiene interacts with the π/ π* of the ethylene to form two new bonding and anti-bonding MOs（[4s + 2s]）, and if the HOMO/LUMO of cis-butadiene interacts with the π*/π of ethylene, the reaction is allowed. This interaction can only happen when these orbitals have the same symmetry and overlap isiginificantly, oherwise, the reaction is forbbidden.

'''Exercise'''

Use the the AM1 semi-empirical molecular orbital method for these calculations (to start with).

'''i)''' Sketch cis butadiene in GaussView -> Calculate: Gaussian -> Job type: opt_freq -> Method: AM1 semi-empirical -> additional keywords: ‘pop=full’ -> Submit.

{| border="2"
|-
! Jmol of cis butadiene
! Results summary
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>jmol of cis butadiene.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:cis butadiene rs_-36.3306.jpg|center|]]
|}

Plot the HOMO and LUMO of cis butadiene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:cis butadiene HOMO_-0.343.jpg|center|]]
E= -0.343 a.u.
|[[Image:cis butadiene LUMO_0.017.jpg|center|]]
E= 0.017 a.u.
|-
| Symmetry w.r.t plane
| Asymmetric
| Symmetric
|}

'''''

The abve procedures have been repeated for ethylene:

{| border="2"
|-
! '''Jmol of cis butadiene'''
! '''Results summary'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>ethylene_JMOL.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ethylene_rs.jpg|center|]]
|}

Plot the HOMO and LUMO of ethylene and determine its symmetry:

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Cis-butadiene'''
|[[Image:ethylene_HOMO_-0.387.jpg|center|]]
E= -0.387 a.u.
|[[Image:ethylene_LUMO_0.052.jpg|center|]]
E= 0.052 a.u.
|-
| Symmetry w.r.t plane
| Symmetric
| Asymmetric
|}

'''ii)''' Computate the Transition State geometry and examine the nature of the reaction path for the prototype reaction.

Based on the optimisied structures in i) -> draw a guess transition state structure(the guessed interfragment distance between the chain end Cs= 2.1A) -> Calculate: Gaussian -> Job type: opt+freq; optimise to a: TS(Berny); calculate force constants: once -> Method: AM1 semi-empirical -> additonal keywords ‘opt=noeigen’.
The optimization was successfully carried out as the output gives only one imaginary vibraitonal frequency.

{| border="2"
|-
! '''Jmol of Transition State geometry'''
! '''Results summary'''
! '''Imaginary frequency'''
|-
||<jmol>
<jmolApplet>
<title>Cyclopentasiloxane</title><color>pink</color><size>150</size>
<uploadedFileContents>sketch.mol</uploadedFileContents>
</jmolApplet>
</jmol>
|[[Image:ts_rs.jpg|center|]]
|[[Image:ts_vb_-955.785.jpg|center|]]
-955.785cm-1
|}

As can be seen the transition structure has an ''envelope''-like shape, since the overlap between the ethylene π/π* orbitals and the HOMO/LUMO of butadiene can be maximized.

Plot the HOMO and LUMO of transition structure and determine its symmetry:

The plane is defined by the horizental middle plane between the cis butadiene and the ethylene

{| border="2"
|-
! /
! '''HOMO '''
! '''LUMO'''
|-
| '''Transition state'''
|[[Image:ivy1.jpg|center|]]
E= -0.323 a.u.
|[[Image:MO_LUMO_0.023.jpg|center|]]
E= 0.023 a.u.
|-
| '''Symmetry w.r.t the plane'''
| Asymmetric
| Symmetric
|}

Plot the HOMO as in (i). Rotate the molecule so that the symmetry and nodal properties of the system can be interpreted, and save a copy of the image.

'''(iii)'''Study the regioselectivity of the Diels Alder Reaction

Cyclohexa-1,3-diene 1 undergoes facile reaction with maleic anhydride 2 to give primarily the endo adduct. The reaction is supposed to be kinetically controlled so that the exo transition state should be higher in energy.
regioslectivity
regioslectivity

Locate the transition structures for both 3 and 4. Compare the energies of the endo and exo forms.

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

'''''

Conclusion:
DFT using a local spin density approximation (S-VWN/6-3 1G*) gives a poor estimate of the activation energy and predicts a diyl-like geometry (d = 1.753 A). The resulting KIEs are in accord with that 'tight" transition structure but differ significantly from experimental values. The nonlocal methods (B-LYP and Becke3-LYP) yield looser "aromatic" chair transition structures (d = 1.98-2.15 A) and much better estimates of the activation energies. Becke3-LYP, using 6-31G* and 6-31 1+G** basis sets, provides estimates of the activation energy within 1 kcal/mol of the
experimental value.

The boat transition structure is calculated by DFT at all levels
to be a looser transition structure by about 0.25 A and to be about
5-6 kcal/mol higher in energy than the chair structure.

==== '''Suggested Discussion''' ====

File:Ivy1.jpg

2009-02-27T09:49:49Z

Yz1506:

File:Ts vb -955.785.jpg

2009-02-27T09:49:24Z

Yz1506:

File:Ts rs.jpg

2009-02-27T09:49:16Z

Yz1506: