ChemWiki - User contributions [en]

Rep:Xiaojie102820

2012-11-02T17:02:17Z

Xt810: /* Further discussion */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049Å || 2.01923Å
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''

[[File:Cs2.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -0..5041985a.u.
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Point group'''

[[File:Cs3.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| point group || Cs
|-
| Energy || -0.05150480 a.u.
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_ENDO.PNG|300px]] || [[File:LUMO_ENDO.PNG|300px]]

|-
| The HOMO is asymmetric with respect to the plane || The LUMO is asymmetric with respect to the plane as well
|}

====Discussion====

{| class="wikitable" border="1"
| ts || C-C space || partly formed C-C bond || other C-C bond
|-
| exo || 2.94510Å ||2.17040Å ||1.48819Å

|-
| endo || 2.89215Å ||2.16232Å ||1.48923Å

|}

'''Structure comparison'''

For the exo transition state, the large maleic anhydride group is located near to the -CH2-CH2- fragment which leads to high steric hindrance.
so the exo-ts is higher in energy(more strained). However, this steric hindrance does not exists for the endo form as the maleic anhydride group is located far away from the beidging carbon fragments. Consequently, the endo adduct will be the major product under kinetic control due to the lower activation barrier.

'''HOMO-LUMO overlap'''

[[File:Momomo.bmp]]

The reaction is allowed due to perfect interaction of the HOMO-LUMO.

'''secondary orbital overlap effect-MO overlap'''

The secondary orbital overlap effect is defined as the positive overlap of the nonactive frontier molecule orbital of a pericyclic reaction.

[[File:Secondary.PNG|450px]]

[[File:Sc.PNG|450px]]

According to the diagram above, it is clear that the P orbitals on the carbonyl carbon atom can overlap with the p orbitals of carbon on diene which leads to the stabilisation of the endo-transition state. While in exo-form, there is no such interaction.

==Further discussion==
Ans: The conditions of the solvent used is neglect when we run the calculation.

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102820

2012-11-02T17:00:04Z

Xt810: /* Discussion */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049Å || 2.01923Å
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''

[[File:Cs2.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -0..5041985a.u.
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Point group'''

[[File:Cs3.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| point group || Cs
|-
| Energy || -0.05150480 a.u.
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_ENDO.PNG|300px]] || [[File:LUMO_ENDO.PNG|300px]]

|-
| The HOMO is asymmetric with respect to the plane || The LUMO is asymmetric with respect to the plane as well
|}

====Discussion====

{| class="wikitable" border="1"
| ts || C-C space || partly formed C-C bond || other C-C bond
|-
| exo || 2.94510Å ||2.17040Å ||1.48819Å

|-
| endo || 2.89215Å ||2.16232Å ||1.48923Å

|}

'''Structure comparison'''

For the exo transition state, the large maleic anhydride group is located near to the -CH2-CH2- fragment which leads to high steric hindrance.
so the exo-ts is higher in energy(more strained). However, this steric hindrance does not exists for the endo form as the maleic anhydride group is located far away from the beidging carbon fragments. Consequently, the endo adduct will be the major product under kinetic control due to the lower activation barrier.

'''HOMO-LUMO overlap'''

[[File:Momomo.bmp]]

The reaction is allowed due to perfect interaction of the HOMO-LUMO.

'''secondary orbital overlap effect-MO overlap'''

The secondary orbital overlap effect is defined as the positive overlap of the nonactive frontier molecule orbital of a pericyclic reaction.

[[File:Secondary.PNG|450px]]

[[File:Sc.PNG|450px]]

According to the diagram above, it is clear that the P orbitals on the carbonyl carbon atom can overlap with the p orbitals of carbon on diene which leads to the stabilisation of the endo-transition state. While in exo-form, there is no such interaction.

==Further discussion==

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102820

2012-11-02T16:54:08Z

Xt810: /* Discussion */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049Å || 2.01923Å
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''

[[File:Cs2.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -0..5041985a.u.
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Point group'''

[[File:Cs3.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| point group || Cs
|-
| Energy || -0.05150480 a.u.
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_ENDO.PNG|300px]] || [[File:LUMO_ENDO.PNG|300px]]

|-
| The HOMO is asymmetric with respect to the plane || The LUMO is asymmetric with respect to the plane as well
|}

====Discussion====

{| class="wikitable" border="1"
| ts || C-C space || partly formed C-C bond || other C-C bond
|-
| exo || 2.94510Å ||2.17040Å ||1.48819Å

|-
| endo || 2.89215Å ||2.16232Å ||1.48923Å

|}

'''Structure comparison'''

For the exo transition state, the large maleic anhydride group is located near to the -CH2-CH2- fragment which leads to high steric hindrance.
so the exo-ts is higher in energy(more strained). However, this steric hindrance does not exists for the endo form as the maleic anhydride group is located far away from the beidging carbon fragments. Consequently, the endo adduct will be the major product under kinetic control due to the lower activation barrier.

'''HOMO-LUMO overlap'''

[[File:Momomo.bmp]]

The reaction is allowed due to perfect interaction of the HOMO-LUMO.

'''secondary orbital overlap effect-MO overlap'''
The secondary orbital overlap effect is defined as the positive overlap of the nonactive frontier molecule orbital of a pericyclic reaction.

[[File:Secondary.PNG|450px]]

[[File:Sc.PNG|450px]]

According to the diagram above, it is clear that the P orbitals on the carbonyl carbon atom can overlap with the p orbitals of carbon on diene which leads to the stabilisation of the endo-transition state.

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

File:Sc.PNG

2012-11-02T16:46:35Z

Xt810:

File:Secondary.PNG

2012-11-02T16:44:37Z

Xt810:

File:Momomo.bmp

2012-11-02T16:36:02Z

Xt810:

Rep:Xiaojie102820

2012-11-02T16:21:24Z

Xt810: /* Discussion */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049Å || 2.01923Å
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''

[[File:Cs2.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -0..5041985a.u.
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Point group'''

[[File:Cs3.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| point group || Cs
|-
| Energy || -0.05150480 a.u.
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_ENDO.PNG|300px]] || [[File:LUMO_ENDO.PNG|300px]]

|-
| The HOMO is asymmetric with respect to the plane || The LUMO is asymmetric with respect to the plane as well
|}

====Discussion====

{| class="wikitable" border="1"
| ts || C-C space || partly formed C-C bond || other C-C bond
|-
| exo || 2.94510Å ||2.17040Å ||1.48819Å

|-
| endo || 2.89215Å ||2.16232Å ||1.48923Å

|}

'''Structure comparison'''

For the exo transition state, the large maleic anhydride group is located near to the -CH2-CH2- fragment which leads to high steric hindrance.
so the exo-ts is higher in energy(more strained). However, this steric hindrance does not exists for the endo form as the maleic anhydride group is located far away from the beidging carbon fragments. Consequently, the endo adduct will be the major product under kinetic control due to the lower activation barrier.

'''Difference in activation energy'''

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102820

2012-11-02T16:10:41Z

Xt810: /* Comparison Table */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049Å || 2.01923Å
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''

[[File:Cs2.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -0..5041985a.u.
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Point group'''

[[File:Cs3.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| point group || Cs
|-
| Energy || -0.05150480 a.u.
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_ENDO.PNG|300px]] || [[File:LUMO_ENDO.PNG|300px]]

|-
| The HOMO is asymmetric with respect to the plane || The LUMO is asymmetric with respect to the plane as well
|}

====Discussion====

{| class="wikitable" border="1"
| ts || C-C space || partly formed C-C bond || other C-C bond
|-
| exo || 2.94510Å ||2.17040Å ||1.48819Å

|-
| endo || 2.89215Å ||2.16232Å ||1.48923Å

|}

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102820

2012-11-02T16:09:46Z

Xt810: /* Discussion */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''

[[File:Cs2.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -0..5041985a.u.
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Point group'''

[[File:Cs3.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| point group || Cs
|-
| Energy || -0.05150480 a.u.
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_ENDO.PNG|300px]] || [[File:LUMO_ENDO.PNG|300px]]

|-
| The HOMO is asymmetric with respect to the plane || The LUMO is asymmetric with respect to the plane as well
|}

====Discussion====

{| class="wikitable" border="1"
| ts || C-C space || partly formed C-C bond || other C-C bond
|-
| exo || 2.94510Å ||2.17040Å ||1.48819Å

|-
| endo || 2.89215Å ||2.16232Å ||1.48923Å

|}

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102820

2012-11-02T16:08:38Z

Xt810: /* Conclusion */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''

[[File:Cs2.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -0..5041985a.u.
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Point group'''

[[File:Cs3.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| point group || Cs
|-
| Energy || -0.05150480 a.u.
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_ENDO.PNG|300px]] || [[File:LUMO_ENDO.PNG|300px]]

|-
| The HOMO is asymmetric with respect to the plane || The LUMO is asymmetric with respect to the plane as well
|}

====Discussion====

Normal 0 false false false EN-GB ZH-CN X-NONE

{| class="wikitable" border="1"
| ts || C-C space || partly formed C-C bond || other C-C bond
|-
| exo || 2.94510 ||2.17040 ||1.48819

|-
| endo || 2.89215 ||2.16232 ||1.48923

|}

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Xiaojie1028

2012-11-02T15:32:57Z

Xt810: Blanked the page

Rep:Xiaojie102820

2012-11-02T15:31:51Z

Xt810: /* Optimisation of endo ts */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''

[[File:Cs2.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -0..5041985a.u.
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Point group'''

[[File:Cs3.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| point group || Cs
|-
| Energy || -0.05150480 a.u.
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_ENDO.PNG|300px]] || [[File:LUMO_ENDO.PNG|300px]]

|-
| The HOMO is asymmetric with respect to the plane || The LUMO is asymmetric with respect to the plane as well
|}

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102820

2012-11-02T15:31:26Z

Xt810: /* Optimisation of endo ts */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''

[[File:Cs2.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -0..5041985a.u.
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Point group'''

[[File:Cs3.PNG]]

'''General Information'''

Normal 0 false false false EN-GB ZH-CN X-NONE

{| class="wikitable" border="1"
| point group || Cs
|-
| Energy || -0.05150480 a.u.
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_ENDO.PNG|300px]] || [[File:LUMO_ENDO.PNG|300px]]

|-
| The HOMO is asymmetric with respect to the plane || The LUMO is asymmetric with respect to the plane as well
|}

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

File:Cs3.PNG

2012-11-02T15:30:48Z

Xt810:

Rep:Xiaojie102820

2012-11-02T15:27:01Z

Xt810: /* Molecule Orbital Analysis */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''

[[File:Cs2.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -0..5041985a.u.
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_ENDO.PNG|300px]] || [[File:LUMO_ENDO.PNG|300px]]

|-
| The HOMO is asymmetric with respect to the plane || The LUMO is asymmetric with respect to the plane as well
|}

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102820

2012-11-02T15:24:45Z

Xt810: /* Optimisation of exo-ts */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''

[[File:Cs2.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -0..5041985a.u.
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102820

2012-11-02T15:23:27Z

Xt810: /* Optimisation of exo-ts */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''
[[File:Cs2.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -0..5041985a.u.
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102820

2012-11-02T15:20:34Z

Xt810: /* Optimisation of exo-ts */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Point group'''
[[File:Cs2.PNG]]

'''General Information'''
Normal 0 false false false EN-GB ZH-CN X-NONE

{| class="wikitable" border="1"
| Energy ||
|-
| point group || Cs
|}
'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

File:Cs2.PNG

2012-11-02T15:20:11Z

Xt810:

Rep:Xiaojie102818

2012-11-02T15:16:54Z

Xt810:

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''General Information'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102820

2012-11-02T15:14:31Z

Xt810: Created page with "==Module 3== In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions. ==The Cope ..."

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''General Information'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T15:12:39Z

Xt810: /* Optimisation of exo-ts */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''General Information'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T15:10:16Z

Xt810: /* Molecule orbital Analysis */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|450px]] || [[File:LUMO_EXO.PNG|450px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T15:09:59Z

Xt810: /* Molecule orbital Analysis */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|400px]] || [[File:LUMO_EXO.PNG|400px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T15:09:38Z

Xt810: /* Molecule orbital Analysis */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_EXO.PNG|600px]] || [[File:LUMO_EXO.PNG|600px]]

|-
| The HOMO is asymmetric w.r.t the plane || The LUMO is asymmetric w.r.t the plane as well
|}

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T15:07:46Z

Xt810: /* Molecule Orbital */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T15:07:08Z

Xt810: /* Molecule Orbital */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T15:06:24Z

Xt810: /* Optimisation of exo-ts */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

Normal 0 false false false EN-GB ZH-CN X-NONE

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T15:05:57Z

Xt810: /* EXO AND ENDO Selectivity */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

Normal 0 false false false EN-GB ZH-CN X-NONE

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

=== The regioselectivity of the Diels Alder Reaction===
====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T15:04:05Z

Xt810: /* Geometry Information */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

Normal 0 false false false EN-GB ZH-CN X-NONE

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T15:03:39Z

Xt810: /* Geometry Information */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif|550px]] || [[File:LOWEST FREQUENCY.gif|550px]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds(not interacting) actually.'''
|}

====Molecule Orbital====

Normal 0 false false false EN-GB ZH-CN X-NONE

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T15:01:17Z

Xt810: /* EXO AND ENDO Selectivity */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

Normal 0 false false false EN-GB ZH-CN X-NONE

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:58:04Z

Xt810: /* EXO AND ENDO Selectivity */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

Normal 0 false false false EN-GB ZH-CN X-NONE

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:57:22Z

Xt810: /* Molecule Orbital */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

Normal 0 false false false EN-GB ZH-CN X-NONE

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO_TS_XIAOJIE.PNG|500px]] || [[File:LUMO TS xiaojie.PNG|500px]]

|-
| The HOMO is asymmetric(a) with respect to the plane. || While the LUMO is symmetric(s).
|}
|}

'''Conclusion'''

The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:53:31Z

Xt810: /* Geometry Information */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The new C-C sigma bond length is 2.1195 Å. It is shorter than the twice of Van Der Waal redius(1.70*2=3.40 Å) which indicates there do has bonds forming between the terminal carbons. However, It is longer than the SP3 and SP2 C-C bond which means that the new sigma bond in the transition state is just partly formed.

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

There is only one imaginary frequency of magnitude 955.70cm-1, again indicates it is a transition state.

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:47:38Z

Xt810: /* Optimisation of the ts */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:47:15Z

Xt810: /* Geometry Information */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:39:12Z

Xt810: /* Optimisation of the ts */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Point group'''

[[File:Cs.PNG]]

'''General information'''

{| class="wikitable" border="1"
| Energy || 0.11165468a.u.
|-
| Point Group || Cs
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

File:Cs.PNG

2012-11-02T14:38:57Z

Xt810:

Rep:Xiaojie102818

2012-11-02T14:35:34Z

Xt810: /* Optimisation of the ts */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''General information'''

{| class="wikitable" border="1"
| Energy ||
|-
| Point Group ||
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:34:25Z

Xt810: /* Optimisation of the ts */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''General information'''
Normal 0 false false false EN-GB ZH-CN X-NONE

{| class="wikitable" border="1"
| Energy ||
|-
| Point Group ||
|}

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:31:30Z

Xt810: /* Transition State geometry for the prototype reaction */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|300px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:31:17Z

Xt810: /* Transition State geometry for the prototype reaction */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG|150px]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:30:58Z

Xt810: /* Transition State geometry for the prototype reaction and an examination of the nature of the reaction path */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction===

[[File:REACTION_222.PNG]]

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

File:REACTION 222.PNG

2012-11-02T14:30:25Z

Xt810:

Rep:Xiaojie102818

2012-11-02T14:22:42Z

Xt810: /* Molecule orbital */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| '''It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane.''' || '''While the LUMO orbital is symmetric(s) with respect to the plane.'''
|}

===Transition State geometry for the prototype reaction and an examination of the nature of the reaction path===

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

'''The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).'''

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:21:55Z

Xt810: /* Molecule orbital */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane. || While the LUMO orbital is symmetric(s) with respect to the plane.
|}

===Transition State geometry for the prototype reaction and an examination of the nature of the reaction path===

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

'''The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).'''

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:20:46Z

Xt810: /* Molecule orbital */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|650px]] || [[File:CIS_BUTA._LUMO.PNG|350PX]]
|-
| It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane. || While the LUMO orbital is symmetric(s) with respect to the plane.
|}

===Transition State geometry for the prototype reaction and an examination of the nature of the reaction path===

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

'''The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).'''

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:20:31Z

Xt810: /* Molecule orbital */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| HOMO || LUMO
|-
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG|350PX]]
|-
| It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane. || While the LUMO orbital is symmetric(s) with respect to the plane.
|}

===Transition State geometry for the prototype reaction and an examination of the nature of the reaction path===

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

'''The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).'''

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>

Rep:Xiaojie102818

2012-11-02T14:18:45Z

Xt810: /* Molecule orbital */

==Module 3==
In this page, I will characterise transition structures on potential energy surfaces for the Cope rearrangement and Diels Alder cycloaddition reactions.

==The Cope Rearrangement Tutorial==
In this section,I will use the Cope rearrangement of 1,5-hexadiene as an example.And my objectives are to locate the low-energy minima and transition structures on the C6H10 potential energy surface, to determine the preferred reaction mechanism.

[[File:Reaction_core_rearrangement.PNG|thumb|[3,3]-sigmatropic shift rearrangement]]

===Molecule1,5-hexadiene===
==== HF/3-21G Optimised (Anti 1) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Aniti opt xiaojie.PNG]]

'''Point group Analysis'''

[[File:Anti pointgroup xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.69260235a.u.
|-
| Point Group || C2
|}
By comparing to the Appendix 1, this structure should be Anti-1.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000825 0.001800 YES
RMS Displacement 0.000314 0.001200 YES
Predicted change in Energy=-2.682036D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/HEX_ANTI_OPT.LOG The log. file of HF/3-21G optimised (anti-1) 1,5-hexadiene]

==== HF/3-21G Optimised (Gauche1) 1,5-hexadiene====
Now I will optimised 1,5-hexadiene molecule with a "gauche" linkage for the central four C atoms. With the previous knowledage from the conformational analysis course(2nd year), the gauche form should be lower in the energy. Unlike small straight molecules which prefer app(anti-periplanar) due to large orbital overlap, the large molecules shift balance to the gauche conformation(given highly proportion of gauche form in large molecules). This incursion of gauche forms is due to the longer distances favouring folding of the chain back upon itself, and hence setting up van der Waals attractions.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAU1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_gauche1_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Gauche1_pointgroup_xiaojie.PNG]]

'''General Information'''

{| class="wikitable" border="1"
| Energy || -231.68771617a.u.
|-
| Point Group ||C2 with a twofold symmetry axis
|}
By checking the Appendix 1, this structure is Gauche-1.

Now we can compare the final energy of this two structures. The 'gauche' linkage is 0.00488618a.u.(about3.066kcal/mol) higher in energy than the 'anti' linkage. This result is different from my prediction. I think there is overestimation of the enetgy for gauche form when we using the 3-21G basis set.

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000466 0.001800 YES
RMS Displacement 0.000111 0.001200 YES
Predicted change in Energy=-1.790991D-09
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/87/HEX_GAU1_OPT.LOG Log.file of HF/3-21G optimised (Gauche-1) structure]

==== Lowest energy conformation-(gauche3)====
Prediction: Based on the results I got from above, I think the anti/gauche/anti conformer might be the lowest energy conformation of 1,5-hexadiene. In order to check the result, I need to optimised the guess structure.

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_GAUCHE3.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Gauche3_summary_Xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Pointgropu_gauch3_Xiaojie.PNG]]

{| class="wikitable" border="1"
| Energy || -231.69266120a.u.
|-
| Point Group || C1
|}

'''The energy I get is -231.69266120a.u. which is lower than the above two structures(check!).'''

'''Comparing the structure in the Appendix table, the conformer which I predict is Gauche-3.'''

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001317 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
Predicted change in Energy=-3.610321D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/d/d6/HEX_GAUCHE.LOG LOG. file of HF/3-21G optimised (gauche-3)structure]

==== HF/3-21G Optimised (Anti2) 1,5-hexadiene====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Tble'''

[[File:Hex_anti2_summary_xiaojie.PNG]]

'''Point Group Analysis'''

[[File:Anti2_pointgroup_xiaojie.PNG]]

'''The energy I got is -231.69253528a.u. which is very colse to the value in the table(-231.69254a.u.).'''

'''The point group is Ci(identical to the one in table).'''

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000476 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
Predicted change in Energy=-2.037252D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f3/HEX_ANTI2_OPT.LOG LOG. file of the HF/3-21G optimised (Anti-2) conformer]

==== B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====
'''This time, I will optimise the anti 2 structure at a higher level of theory.'''

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>HEX_ANTI2_REOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Hex_anti_reopt_xiaojie.PNG]]

'''Point Group'''

[[File:Anti2 repot pg xiaojie.PNG]]

'''The energy decreased to -234.61170280a.u. And the point group is Ci.'''

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000219 0.001800 YES
RMS Displacement 0.000079 0.001200 YES
Predicted change in Energy=-1.588886D-08
Optimization completed.
-- Stationary point found.</pre>

'''geometry Comparison'''

{| class="wikitable" border="1"
|+
! No. !! HF/3-21G !! B3LYP/6-31*
|-
| c=c Bond length || 1.31613Å || 1.33352Å
|-
| C13-C10-C7 || 126.8060C || 125.2870C
|}

The bond length of the carbon-carbon double bond is lengthened, while, the bond length of the carbon-carbon single bond is shortened on the B3LYP/6-31G* calculation.

The B3LYP/6-31G* method has a better basis set than the HF/3-21G method,gives a better aggrement with the experiment value.

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9a/HEX_ANTI2_REOPT.LOG LOG. file of B3LYP/6-31G* Optimised (Anti2)conformer]

==== Frequency Analysis of B3LYP/6-31G* Optimised (Anti2) 1,5-hexadiene====

'''The final energies given represent the energy of th molecule on the bare potential energy surface. In order to compare these energies with experimental value, the frequency calculation is required.'''

'''vibrational frequencies'''

[[File:Anti_631.PNG]]

'''It is clear that there is no imaginary frequencies, only real ones which confirms it is a minimum(the frequency analysis is essentially the second derivative of the potential energy surface, if the frequencies are all positive then we have a minimum).'''

'''IR spectrum'''

[[File:IR_anti2__xiaojie.PNG|400px]]

'''File'''

<pre>Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500821</pre>

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/6e/-HEX_ANTI2_631G_FRE-_view_file.txt Frequency file of anti2 conformer]

=="Chair" and "Boat" Transition Structures==
In this section I will set up a transition structure optimization.

=== allyl fragment ===

''' HF/3-21G ''' optimised allyl fragement

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>ALLYLCHAIR_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Allyl_summary.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000048 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000141 0.001800 YES
RMS Displacement 0.000070 0.001200 YES
Predicted change in Energy=-1.277267D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/b/b9/ALLYLCHAIR_OPT.LOG Log. file of optimised allyl]

===Chair transition state-guess structure===
Now we are going to optimise the transition state. Actually,the transition states correspond to saddle points with one negative second derivative on the potential energy surface. So in order to locate the transition state we can find a point with one negative second derivative(which is one imaginary frequency in this experiment). The reason why transition state optimisation is more difficult than that of minimum is that a successful search should start off in a region where the reaction coordinate already has a negative curvature.(which I did at second year lab: search for a transition state should start near the transition state!)

====Optimisation of chair-ts in 3-21G====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Guess_ts_opt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001401 0.001800 YES
RMS Displacement 0.000201 0.001200 YES
Predicted change in Energy=-1.246508D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/75/GUESS_TS_OPT.LOG Log. file of 3-21G optimised chair ts]

'''Frequency Analysis'''

'''Vibrational Frequency'''

[[File:Vf_321g_chair.PNG]]

The frequency calculation gives an(only one) imaginary frequency of magnitude 817.98 cm-1. It means that the guess transition state is reasonable(reason explained above).

'''Animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Animation_321g_chair.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -817.98 || 5.8659 || C2h
|}

'''File'''

<pre>Sum of electronic and zero-point Energies= -231.466702
Sum of electronic and thermal Energies= -231.461342
Sum of electronic and thermal Enthalpies= -231.460398
Sum of electronic and thermal Free Energies= -231.495208</pre>

====Optimisation of chair-ts by using the frozen coordinate method====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_OPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''CHK file'''

[[File:CHK.PNG]]

The optimized structure looks a lot like the transition I got by using 3-21G. However, bond forming/breaking distances are fixed to 2.2 Å.

'''Summary table'''

[[File:Fro_chair_xiaojie.PNG]]

The final energy here is -231.61499866a.u.which is greater than the one in the HF/3-21G.

'''Output file'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000512 0.001800 YES
RMS Displacement 0.000088 0.001200 YES
Predicted change in Energy=-3.015680D-08
Optimization completed.
-- Stationary point found.</pre>
'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/86/GUESS_TS_FROZEN_OPT.LOG File of frozen coordinate method optimised chair ts]

====Reoptimisation after Redundant Coord Editor====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>GUESS_TS_FROZEN_reOPT.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:2ndfro_chair_xiaojie.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.001240 0.001800 YES
RMS Displacement 0.000244 0.001200 YES
Predicted change in Energy=-6.076100D-07
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/9/9b/GUESS_TS_FROZEN_OPT2ND.LOG File of reoptimised chair ts after RCE]

'''chk'''

[[File:Bong_length_chair_frozen_2nd.PNG]]

'''bond forming/bond breaking bond length is 2.01923 Å'''

====Comparison Table====

{| class="wikitable" border="1"
|+
! hf/3-21g !! After RCE
|-
| 2.02049 || 2.01923
|}

===Boat transition state===
We are going to optimise the boat transition state using QST2 method. It requires that the reactants and products are numbered in the same way.

====Reactant/product-QST2 calculation====

<jmol><jmolApplet>
<title>test molecule</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>Reactant_boat_optfrequ.mol</uploadedFileContents>
</jmolApplet></jmol>

'''Summary Table'''

[[File:Reactant_freopt.PNG]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000094 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001626 0.001800 YES
RMS Displacement 0.000525 0.001200 YES
Predicted change in Energy=-4.528634D-08
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/cd/REACTANT_BOAT_OPTFRE.LOG File of QST2 optimised reactant]

'''Vibrational Analysis'''

[[File:Boat__vf.PNG]]

There is only one imaginary frequency of magnitude of 839.84cm-1(confirms it is a transition state).

'''Animation'''

'''IR Spectrum'''

[[File:Reactant.PNG]]

'''Output File'''
<pre>Sum of electronic and zero-point Energies= -231.450926
Sum of electronic and thermal Energies= -231.445297
Sum of electronic and thermal Enthalpies= -231.444352
Sum of electronic and thermal Free Energies= -231.479772</pre>

===IRC Analysis of Chair Transition state===
Since I have known the optimised chair and boat structure, here is a problem raised: Which conformers of 1,5-hexadiene do they connect? And I find it is hard to predict which conformer the reaction paths from the transitions structures will lead to. So in this section, I will run the IRC method which allows me to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

[[File:Chair_irc.gif]]

[[File:Irc_1_summary.PNG]]

'''irc pathway'''

[[File:IRC_pathway.PNG|800px]]

There are 27 intermediate geometries. According to the IRC pathway diagram ,we start from the transition state(red circled point on the graph) and the energy goes down towards the minimum with the deepest gradient.However, it hasn't reached the minimum geometry and it stopped! So In order to get the minimum, I can take the last point on the IRC and run a normal minimization(optimisation).

'''Run minimization'''

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Optafterirc.mol</uploadedFileContents> </jmolApplet></jmol>
'''Summary Table'''

[[File:IRC_MINIUM_SUMMARY.PNG|300px]]

'''Point Group'''

[[File:Ater_ircpoint_group.PNG]]

After the optimisation, the final gradient decreased to 0.00000256. In addition,the final energy is -231.69167a.u. and the point group is C2. Now we can look up the Appendix table, the structure we get is Gauche-2!(the conformer that chair and boat connect).

===Optimisation of Chair and Boat by using B3LYP/6-31G*===

Finally I will calculate the activation energies for our reaction via both transition structures.

====B3LYP/6-31G* optimised Chair transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>CHAIR TS GUESS XIAOJIE 631g.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:CHAIR TS GUESS XIAOJIE 631g summary.PNG]]

'''Output File'''

<pre> Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000829 0.001800 YES
RMS Displacement 0.000115 0.001200 YES
Predicted change in Energy=-7.523575D-08
Optimization completed.
-- Stationary point found.
</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f1/CHAIR_TS_GUESS_XIAOJIE.LOG B3LYP/6-31G* optimised Chair ts log. file B3LYP/6-31G optimised chair ts]

====B3LYP/6-31G* optimised Boat transition state====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>PRODUCT_OPTFRE_631G.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Boat_summary.PNG‎]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000304 0.000450 YES
RMS Force 0.000074 0.000300 YES
Maximum Displacement 0.001756 0.001800 YES
RMS Displacement 0.000780 0.001200 YES
Predicted change in Energy=-1.694834D-06
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/8/8f/PRODUCT_OPTFRE_631G.LOG Log. file of B3LYP/6-31G optimised Boat ts]

===Frequency analysis of B3LYP/6-31G*optimised transition state===
====Chair TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.414931
Sum of electronic and thermal Energies= -234.409010
Sum of electronic and thermal Enthalpies= -234.408066
Sum of electronic and thermal Free Energies= -234.443817</pre>

'''IR spectrum'''

[[File:IR_631gfre.PNG]]

'''Vibration frequency'''

[[File:Chair__631g_xiaojie.PNG]]

It is clear that there is only one imaginary frequency(-565.72) which again confirms it is a transition state.

'''Vibrational animation'''

{| class="wikitable" border="1"
|+
! No. !! Form of the vibration !! Discription !! frequency !! intensity !! symmetry D3h point group
|-
| 1 || [[File:Chair_ts_631g.PNG |150px]] || The two pair terminal carbons are moving in concerned direction, but in opposite direction( bond making and bond breaking occur synchronously). || -565.72 || 0.0803 || C2h
|}

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/f/f0/CHAIR_TS_GUESS_XIAOJIE_631G_FRE.LOG Frequency output file of 6-31G* optimised chair ts]

====Boat TS====

'''Output File'''

<pre>Sum of electronic and zero-point Energies= -234.402318
Sum of electronic and thermal Energies= -234.395985
Sum of electronic and thermal Enthalpies= -234.395041
Sum of electronic and thermal Free Energies= -234.431729</pre>

'''Vibrational Frequency'''

[[File:Boat_631g_vf.PNG]]

'''IR Spectrum'''

[[File:Boat_IR631g.PNG|500px]]

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/7/79/PRODUCT_OPTFRE_631G_FRE.LOG Frequency output file of optimised boat ts]

====Result Table====
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932243
| align="center" | -231.466702
| align="center" | -231.461342
| align="center" | -234.55698283
| align="center" | -234.414931
| align="center" | -234.409010
|-
| '''Boat TS'''
| align="center" | -231.60280245
| align="center" | -231.450926
| align="center" | -231.445297
| align="center" | -234.54309090
| align="center" | -234.402318
| align="center" | -234.395985
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253528
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.61170280
| align="center" | -234.469212
| align="center" | -234.461856
|}

 *1 hartree = 627.509 kcal/mol 

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.98
| align="center" | 41.33
| align="center" | 44.7 ± 2.0
|}

 
Ater comparing the activation energy of two basis set, it is clear that although the geometries are reasonably similar, energy differences are markedly different! Moreover, activation energies calculated at BYLYP/6-31G* are in good aggrement with the experiment value. Finally, the activation energy of the chair ts is about10kJ/mol lower than that of the boat transition state(small barrier!). So the reaction will more likely to proceed via a chair transition state.

==The Diels Alder Cycloaddition==
In this exercise, I will characterise transition structures using the method I have learned in the tutorial part. The Diels–Alder reaction is an organic chemical reaction (specifically, a cycloaddition) between a conjugated diene and a substituted alkene,to form a substituted cyclohexene system. The HOMO-LUMO overlap can be used to perdict whether the reaction occur or not.

=== cis butadiene===

====AM1 optimised ciabutadiene====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>AM1_OPT_CISBUTDIENE.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:AM1_OPT_cisbutadiene_summary.PNG]]

[[File:Pg.PNG]]
{| class="wikitable" border="1"
| Energy || 0.04879719a.u.
|-
| Point group || C2v
|}

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000360 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
Predicted change in Energy=-9.691168D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/6/69/AM1_OPT_CISBUTDIENE.LOG File Link of AM1 optimised cisbutadiene]

====Molecule orbital====

{| class="wikitable" border="1"
| [[File:HOMO cis butadiene xiaojiet.PNG|550px]] || [[File:CIS_BUTA._LUMO.PNG]]
|-
| It is clear that the HOMO orbital of cic-butadiene is asymmetric(a) with repect to the plane. || While the LUMO orbital is symmetric(s) with respect to the plane.
|}

===Transition State geometry for the prototype reaction and an examination of the nature of the reaction path===

====Optimisation of the ts====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>Ts opt_xiaojie.mol</uploadedFileContents> </jmolApplet></jmol>
[[File:Ts_alder.PNG|250px|thumb|A Gaussview image(chk.file) of an optimised transition state]]

'''Summary Table'''

[[File:Ts_opt_summary.PNG|300px]]

'''Output file'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000065 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001005 0.001800 YES
RMS Displacement 0.000240 0.001200 YES
Predicted change in Energy=-2.489584D-08
Optimization completed.
-- Stationary point found.</pre>

====Geometry Information====
{| class="wikitable" border="1"
|+ Bond length Comparison
! partly formed sigma C-C bond !! SP3 C-C bond !! SP2 C-C bond !! Van Der Waal radius of C atom
|-
| 2.1195 Å || 1.54000 Å<ref name="1.54000" /> || 1.35520 Å<ref name="1.35520" /> || 1.70 Å<ref name="1.70" />
|}

The dihedral angle is 59.7720

'''The new C-C sigma bond length is 2.1195 Å. It is longer than the SP3/SP2 hybirdised bond, but shorter than the Van Der Waal bond length(1.70*2) which is 3.40 Å. So in the transition state, the two new sigma bonds are NOT fully formed sigma bond(partly formed bond).'''

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/TS_opt.LOG File of optimised transition state]

'''Vibrational frequency'''

[[File:TS_VF.PNG]]

'''There is only one imaginary frequency of magnitude 955.70cm-1->transition state.'''

{| class="wikitable" border="1"
|+
! Animation for imaginary frequency !! Animation for lowest positive frequency
|-
| [[File:IMAGINARY_FREQUENCY.gif]] || [[File:LOWEST FREQUENCY.gif]]
|-
| Two pairs of terminal c-c bonds are moving in and out at the same time. In addition,the two forming bonds had the same bond length of 2.1195. So both bonds are formed to exactly the same extent in the transition statewhich means it is a synchronous concerned reaction. || For the lowest vibrational frequency, the two molecules are just vibrating ,not forming bonds actually.'''
|}

====Molecule Orbital====

'''HOMO'''

[[File:HOMO_TS_XIAOJIE.PNG|500px]]

'''The HOMO is asymmetric(a) with respect to the plane.'''

'''LUMO'''

[[File:LUMO TS xiaojie.PNG|500px]]

'''While the LUMO is symmetric(s).'''

'''Conclusion'''

'''The symmetry of the HOMO at transition state can be found from the MO diagram above. It is clear that the HOMO is asymmetric.The LUMO of ethylene and the HOMO of the butadiene are both a. Thurs it is the HOMO-LUMO pairs of orbital that interact. The reaction is allowed because the HOMO of butadiene can interact with the LUMO of the ethylene;in other words, the HOMO(butadiene)and LUMO(ethylene) have the same symmetry.'''

{| class="wikitable" border="1"
|+
! ethylene !! butadiene
|-
| [[File:LUMO_ETHYLENE.PNG|200px|thumb|LUMO of ethylene]] || [[File:HOMO cis butadiene xiaojiet.PNG|200px|thumb|HOMO of cis butadiene]]
|-
| asymmetric || asymmetric
|}

'''HOMO-LUMO interact-chemdraw(HOMO Of cis butadiene and LUMO of ethylene)'''

[[File:MO_xiaojie.bmp]]

'''Approach with the ethylene under diene.'''

===EXO AND ENDO Selectivity===

'''When both the diene and the dienophile are suitably substituted, a stereochemical feature arises because the reactants may approach each other in two distinct orientations. The substituent on the dienophile may be directed away from the diene (exo approach) or toward the diene (endo approach).'''

====Exo transition state====

=====Optimisation of exo-ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>EXO 3.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Exo__3opt_summary.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000075 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-1.459715D-10
Optimization completed.
-- Stationary point found.</pre>

'''Vibrational frequency'''

[[File:Exo_vf.PNG]]

'''There is only one imaginary frequency of magnitude of 812.19cm-1, again confirms it is a transition state.'''

'''File link'''

[https://wiki.ch.ic.ac.uk/wiki/images/3/32/EXO_3.LOG File of optimised exo-transition state]

=====Molecule orbital Analysis=====

'''HOMO'''

[[File:HOMO_EXO.PNG|600px]]

'''The HOMO is asymmetric w.r.t the plane'''

'''LUMO'''

[[File:LUMO_EXO.PNG|600px]]

'''The LUMO is asymmetric w.r.t the plane as well.'''

====ENDO transition state====

=====Optimisation of endo ts=====

<jmol><jmolApplet> <title>test molecule</title> <color>black</color> <size>200</size> <uploadedFileContents>ENDO_TS_OPT.mol</uploadedFileContents> </jmolApplet></jmol>

'''Summary Table'''

[[File:Summary_endo.PNG]]

'''Output File'''

<pre>Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000194 0.001800 YES
RMS Displacement 0.000054 0.001200 YES
Predicted change in Energy=-2.030039D-09
Optimization completed.
-- Stationary point found.</pre>

'''File Link'''

[https://wiki.ch.ic.ac.uk/wiki/images/c/c9/ENDO_TS_OPT.LOG File link of optimised endo transition state]

=====Molecule Orbital Analysis=====

''''HOMO'''

[[File:HOMO_ENDO.PNG|300px]]

'''The HOMO is asymmetric with respect to the plane.'''

'''LUMO'''

[[File:LUMO_ENDO.PNG|300px]]

'''The LUMO is asymmetric with respect to the plane as well.'''

====Conclusion====

== References ==

<references> <ref name="1.70">^ a b c Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51.[http://pubs.acs.org/doi/abs/10.1021/j100785a001 ] </ref>
<ref name="1.35520">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. .</ref>
<ref name="1.54000">Fox, Marye Anne; Whitesell, James K. (1995). Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen. Springer. </ref>
</references>