2012-11-02T16:06:02Z

Wx610: /* Comparison */

== The Cope Rearrangement ==
=== Optimizing the Reactants and Products ===
==== 1,5-hexadiene with an "anti" linkage ====
The "anti" 1,5-hexadiene was optimized at the '''HF/3-21G''' level of theory with memory limit of '''250MB'''. The followings are the summary, symmetry group and molecule structure of the structure:
===== Molecule =====
<jmol><jmolApplet> <title>"Anti" 1,5-hexadiene molecule</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 15 HEXADIENE ANTI.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN 15 HEXADIENE ANTI OPT SUMMARY byCOMPUTER.PNG|thumb|center|500px|Optimization summary of the "anti" 1,5-hexadiene.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000442 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
===== Symmetry group =====
[[Image:WENMIN 15 HEXADIENE ANTI OPT SYMMERTRY.PNG|thumb|center|500px|Symmetry of the "anti" 1,5-hexadiene.]]
===== File Link =====
[[File:WENMIN 15 HEXADIENE ANTI.LOG]]

==== 1,5-hexadiene with an "gauche" linkage ====
The "gauche" form of 1,5-hexadiene should have lower energy than the "anti" one.
The "gauche" 1,5-hexadiene was optimized at the '''HF/3-21G''' level of theory with memory limit of '''250MB'''. The followings are the summary and symmetry of the structure:
===== Molecule =====
<jmol><jmolApplet> <title>"Gauche" 1,5-hexadiene molecule</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN Log 64127(15 HEXADIENE GAUCHE).mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN 15 HEXADIENE GAUCHE OPT SUMMARY.PNG|thumb|center|500px|Optimization summary of the "gauche" 1,5-hexadiene.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000174 0.001800 YES
RMS Displacement 0.000055 0.001200 YES
===== Symmetry group =====
[[Image:WENMIN 15 HEXADIENE GAUCHE OPT SYMMERTRY.PNG|thumb|center|500px|Symmetry of the "gauche" 1,5-hexadiene.]]
===== File Link =====
[[File:WENMIN Log 64127(15 HEXADIENE GAUCHE).log]]

==== Lowest energy conformation ====
The lowest energy conformation should be the gauche3 form (shown in the Appendix 1<ref name=Appendix />). This form is drawn and optimized at the '''HF/3-21G''' level with memory limit of '''250MB'''. The followings are the results:
===== Molecule =====
<jmol><jmolApplet> <title>1,5-hexadiene molecule with lowest energy</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 15 HEXADIENE GAUCHE 3.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN 15 HEXADIENE GAUCHE 3 SUMMARY.PNG|thumb|center|500px|Optimization summary of the 1,5-hexadiene with lowest energy.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001316 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
===== Symmetry group =====
[[Image:WENMIN_15_HEXADIENE_GAUCHE_3_SYMMETRY.PNG|thumb|center|500px|Symmetry of the 1,5-hexadiene with lowest energy.]]
===== File Link =====
[[File:WENMIN_15_HEXADIENE_GAUCHE_3.LOG]]

==== Structure table ====
Structures and energies are compared with the reference<ref name="reference" />, conformers are identified with specific names.
 

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Conformer'''
| width="150" | '''Structure'''
| width="100" | '''Point Group'''
| width="200" | '''Energy/Hartrees HF/3-21G'''
|- align="center"
| Section 1.1.2: ''gauche2''
|
[[Image:WENMIN 15 HEXADIENE GAUCHE OPT MOLECULE.PNG|150px]]
| C2
| -231.69166702
|- align="center"
| Section 1.1.3: ''gauche3''
|
[[Image:WENMIN_15_HEXADIENE_GAUCHE_3_MOLECULE.PNG‎|150px]]
| C1
| -231.69266120
|- align="center"
| Section 1.1.1: ''anti2''
|
[[Image:WENMIN 15 HEXADIENE ANTI MOLECULE.PNG|150px]]
| Ci
| -231.69253528
|- align="center"
|}

 

From the table shown above, we get that gauche3 conformation has the lowest energy, followed by anti2 conformation. The gauche2 conformation has the highest energy here.

We usually have the impression that anti2 conformation should be lowest in energy level for allyl groups. This is mainly because, for small allyl molecules, the anti-periplanar form has the maximizing σC-H/σ*C-H and/or σC-C/σ*C-C conjugation. In addition, the app form relieves the torsional strain. However, as the allyl molecule number increases, gauche form becomes promoted. This is due to the longer distances favoring van der Waals (dispersion) interaction by folding chain back upon itself. In this case, alkene group results in fewer H groups on the sp2 carbon and some bond angles are wider. This leads to reduce hindrance and avoid the H...H contacts of smaller than 2.1Å at which point hydrogen becomes repulsive. What's more, better overlap of πC=C/σ*C=C results in larger stabilizing energy.

==== Reoptimization of "anti2" conformation of 1,5-hexadiene ====
The "anti2" conformation is reoptimized at the '''B3LYP/6-31G(d)''' level. The followings are the results:
===== Molecule =====
<jmol><jmolApplet> <title>"Anti2" 1,5-hexadiene molecule</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 15 HEXADIENE ANTI REOPT.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN_15_HEXADIENE_ANTI_REOPT_SUMMARY.PNG|thumb|center|500px|Reoptimization summary of the "anti2" 1,5-hexadiene at higher level.]]
===== Output information =====
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
===== Symmetry group =====
[[Image:WENMIN 15 HEXADIENE ANTI REOPT SYMMETRY.PNG|thumb|center|500px|Symmetry of the "anti2" 1,5-hexadiene at higher level.]]
The symmetry group changes to C2h at the '''B3LYP/6-31G(d)''' level from Ci at the '''HF/3-21G''' level.
===== File Link =====
[[File:WENMIN_15_HEXADIENE_ANTI_REOPT.LOG‎]]

==== Frequency of "anti2" conformation of 1,5-hexadiene ====
The frequency of the "anti2" conformation is calculated at the '''B3LYP/6-31G(d)''' level. The followings are the results:
===== Summary =====
[[Image:WENMIN 15 HEXADIENE ANTI FREQ SUMMARY.PNG|thumb|center|500px|Frequency summary of the "anti2" 1,5-hexadiene at higher level.]]
===== Frequencies =====
All is real frequencies, no imaginary ones.
[[Image:WENMIN_15_HEXADIENE_ANTI_FREQ_VIBRATION.PNG|thumb|center|300px]]
===== Energy lists =====
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
===== IR =====
[[Image:WENMIN 15 HEXADIENE ANTI FREQ IR.PNG|thumb|center|1000px|IR spectrum of the "anti2" 1,5-hexadiene at higher level.]]
===== File Link =====
[[File:WENMIN 15 HEXADIENE ANTI FREQ.LOG]]

=== Optimizing the "Chair" and "Boat" Transition ===
==== Allyl fragment optimization ====
The allyl fragment (CH2CHCH2) is optimized at the '''HF/3-31G''' level of theory. The followings are the results:
===== Molecule =====
<jmol><jmolApplet> <title>Allyl fragment</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR OPT 321G.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN A ALLYL OPT 321G SUMMARY.PNG|thumb|center|500px|Optimization summary of the allyl fragment.]]
===== Output information =====
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
===== File Link =====
[[File:WENMIN CHAIR OPT 321G.LOG]]

==== Guess TS optimization and frequency ====
The guess TS is made from two allyl fragments with approximately 2.2Å terminal ends. Then the guess TS is calculated under '''Opt+Freq''' job type, with '''Optimization to a TS (Berny)''', calculate the force constants '''Once''', and type '''Opt=NoEigen''' in the Additional keyword box. The followings are the results:
===== Molecule =====
<jmol><jmolApplet> <title>Guess TS</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR TS GUESS.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN B TS GUESS 321G OPT+FREQ SUMMARY.PNG|thumb|center|500px|Optimization summary of the guess TS.]]
===== Output information =====
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
===== Vibration frequencies =====
There's only one imaginary frequency of magnitude 817.98 cm-1, conforming that this geometry is a TS.
[[Image:WENMIN B TS GUESS 321G OPT+FREQ VIBRATION.PNG|thumb|right|500px]]
[[File:WENMIN_B_CHAIR_TS_VIBRATION.gif‎]]

===== Bond distance =====
The bond distances of terminal ends change to about 2.02Å, as shown in the following two diagrams.
[[Image:WENMIN B TS GUESS BondDistance1.PNG|thumb|center|300px]]
[[Image:WENMIN B TS GUESS BondDistance2.PNG|thumb|center|300px]]

===== File Link =====
[[File:WENMIN CHAIR TS GUESS.LOG]]

==== Guess TS optimization using the frozen coordinate method ====
The guess TS is optimized at the '''HF/3-31G''' level of theory, with minimum optimization and the '''Freeze Coordinate''' under '''Bond'''. However, the Gaussian program doesn't respond to the input of 2.20Å fixed bond length. The result obtained does not have 2.20Å terminal ends although they are very close to 2.20Å.
[[Image:WENMIN C TS GUESS 321G OPT FREEZE BondDistance1.PNG|thumb|center|300px]]
[[Image:WENMIN C TS GUESS 321G OPT FREEZE BondDistance2.PNG|thumb|center|300px]]
So I redo the calculation, but this time with fixed 2.20Å terminal ends using "''Modify Bond''" tool. The followings are the results of second trail:
===== Molecule =====
<jmol><jmolApplet> <title>Guess TS with frozen coordinate</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR TS GUESS OPT C NEW FIXED22.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN Summary.PNG|thumb|center|500px|Optimization summary of the guess TS with frozen coordinate.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001213 0.001800 YES
RMS Displacement 0.000247 0.001200 YES
===== Vibration frequencies =====
There's only one imaginary frequency, conforming that this geometry is a TS.
[[Image:WENMIN C frequency.PNG|thumb|center|500px]]
===== Bond distance =====
This time the length between two terminal ends is exactly 2.20Å, as shown in the following two diagrams.
[[Image:WENMIN Bondlength1.PNG|thumb|center|300px]]
[[Image:WENMIN Bondlength2.PNG|thumb|center|300px]]
===== File Link =====
[[File:WENMIN CHAIR TS GUESS OPT C NEW FIXED22.LOG]]

==== Guess TS optimization using the derivative coordinate method ====
The guess TS obtained from the frozen coordinate method is optimized at the '''HF/3-31G''' level of theory, with minimum optimization and the '''Derivative''' under '''Bond'''. The followings are the results:
===== Molecule =====
<jmol><jmolApplet> <title>Guess TS with derivative coordinate</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR TS GUESS OPT D.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN D TS GUESS 321G OPT FREEZE SUMMARY.PNG|thumb|center|500px|Optimization summary of the guess TS with derivative coordinate.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001154 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
===== Vibration frequencies =====
There's only one imaginary frequency, conforming that this geometry is a TS. The magnitude of the imaginary frequency is 818.06 cm-1, which is very close to the one got from section 1.2.2.
[[Image:WENMIN D frequency.PNG|thumb|center|500px]]
===== Energy list =====
Sum of electronic and zero-point Energies= -231.466693
Sum of electronic and thermal Energies= -231.461334
Sum of electronic and thermal Enthalpies= -231.460390
Sum of electronic and thermal Free Energies= -231.495198
===== Bond distance =====
The bond distances of terminal ends change to about 2.02Å, as shown in the following two diagrams. When comparing the structures obtained from section 1.2.2 and this section, they are almost identical, both having approximate 2.02Å bond distances between terminal ends. This shows that both methods are good approach to determine the TS, since this is a pretty good "guess" of the transition state structure.
[[Image:WENMIN D TS GUESS 321G OPT FREEZE BondDistance1.PNG|thumb|center|300px]]
[[Image:WENMIN D TS GUESS 321G OPT FREEZE BondDistance2.PNG|thumb|center|300px]]

===== File Link =====
[[File:WENMIN CHAIR TS GUESS OPT D.LOG]]

==== Boat TS optimization using the QST2 method ====
The reactant and product are calculated under '''Opt+Freq''' job type with '''Optimization to a TS (QST2)''', using the structures shown as below.
[[Image:WENMIN E REAC+PROC TS QST2 MOLECULE.PNG|thumb|center|500px]]
The followings are the results:
===== Molecule =====
<jmol><jmolApplet> <title>Reactant</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR REAC TS E NEVER.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>Product</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR PROD TS E NEVER.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
NOTE: Ignore the "Chair" under file name. These are boat structures.
[[Image:WENMIN E REAC TS QST2 SUMMARY.PNG|thumb|center|500px|Optimization summary of reactant.]]
[[Image:WENMIN E PROC TS QST2 SUMMARY.PNG|thumb|center|500px|Optimization summary of product.]]
===== Output information =====
Reactant:
Item Value Threshold Converged?
Maximum Force 0.000105 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.001249 0.001800 YES
RMS Displacement 0.000277 0.001200 YES

Product:
Item Value Threshold Converged?
Maximum Force 0.000105 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.001249 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
===== Energy list =====
Reactant:
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445294
Sum of electronic and thermal Enthalpies= -231.444349
Sum of electronic and thermal Free Energies= -231.479768

Product:
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445294
Sum of electronic and thermal Enthalpies= -231.444349
Sum of electronic and thermal Free Energies= -231.479768
===== Vibration frequencies =====
There's only one imaginary frequency, conforming that this geometry is a TS (for reactant and product approach).
[[Image:WENMIN E frequency reactant.PNG|thumb|center|500px|Vibration frequencies of reactant.]]
[[Image:WENMIN E frequency product.PNG|thumb|center|500px|Vibration frequencies of product.]]
Since the structure of reactant and product is exactly the same, all results are the same.
===== File Link =====
Reactant: [[File:WENMIN CHAIR REAC TS E.LOG]]

Product: [[File:WENMIN CHAIR PROD TS E.LOG]]

==== Chair TS IRC ====
The '''IRC''' ('''Intrinsic Reaction Coordinate''') method is used to follow the minimum energy path from a transition structure down its local minimum on a potential energy surface. The optimized chair TS (with derivative bond in this case) is calculated at '''HF/3-21''' level with '''IRC''' under the '''Job Type''' tab. Compute it in the forward direction, calculate the force constants once and change the number of points along the IRC into 50.
===== IRC result =====
[[Image:WENMIN_Irc_movie.gif‎|thumb|center|300px]]
[[Image:WENMIN Ircpath1.PNG‎|thumb|center|500px|Total energy along IRC]]
[[Image:WENMIN Ircpath2.PNG‎|thumb|center|500px|RMS Gradient Norm along IRC]]
44 intermediate geometries are obtained and the last one has the energy of -231.69157861 a.u.
[[Image:WENMIN F CHAIR TS IRC FROM D.PNG|thumb|center|500px]]
===== Options to reach minimum geometry =====
Then three options are tested receptively to get a minimum conformation.

(i) The last point on the IRC is taken to do a minimum optimization and the energy obtained is -231.69166702 a.u, which is lower than -231.69157861 a.u.
[[Image:WENMIN F1 CHAIR TS IRC OPT.PNG|thumb|center|500px]]
(ii) The chair TS is run an IRC again, but this time with 100 points instead of 50. However, the same result is obtained as the original one (50 points), having 44 intermediate geometries with minimum energy of -231.69157861 a.u. (I try to run this with additional note of maxcycles=50, but the result is unchanged.)
[[Image:WENMIN F2 CHAIR TS IRC FROM D 100.PNG|thumb|center|500px]]
(iii) Redo the IRC specifying that compute the force constant at every step. The job is incomplete, resulting only 21 intermediate geometries.
[[Image:WENMIN F3 CHAIR TS IRC FROM D EVERYSTEP.PNG|thumb|center|500px]]
Overall, the step (i) is the only approach actually works, ending up with the conformation of energy -231.69166702 a.u.

===== File link =====
IRC: [[File:WENMIN CHAIR TS IRC F FROM D ALWAYS.LOG]]

Optimization after IRC: [[File:WENMIN CHAIR TS IRC F1 FROM D OPT.LOG]]

Redo IRC with "n=100": [[File:WENMIN CHAIR TS IRC F2 FROM D ALWAYS.LOG]]

Redo IRC with "compute force constants at every step": [[File:WENMIN CHAIR TS IRC F3 FROM D ONCE.LOG]]

==== Boat & Chair TS reoptimization at higher level ====
The chair and boat transition structures are reoptimized using the '''B3LYP/6-31G(d)''' level of theory and carry out the frequency calculations.
===== Boat TS reoptimization at higher level =====
====== Molecule ======
<jmol><jmolApplet> <title>Boat TS molecule</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN_BOAT_TS_REAC_631G_TSONCENOEIGEN.mol</uploadedFileContents> </jmolApplet></jmol>
====== Summary ======
[[Image:WENMIN G BOAT 631G REOPT SUMMARY.PNG|thumb|center|500px|Reoptimization summary of the boat TS at higher level.]]
====== Output information ======
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001276 0.001800 YES
RMS Displacement 0.000316 0.001200 YES
====== Energy list ======
Sum of electronic and zero-point Energies= -234.402336
Sum of electronic and thermal Energies= -234.396003
Sum of electronic and thermal Enthalpies= -234.395059
Sum of electronic and thermal Free Energies= -234.431745
====== File Link ======
Reoptimization: [[File:WENMIN BOAT TS REAC 631G TSONCENOEIGEN.LOG‎]]

Frequency: [[File:WENMIN BOAT TS REAC 631G FREQ.LOG]]

===== Chair TS reoptimization at higher level =====
====== Molecule ======
<jmol><jmolApplet> <title>Chair TS molecule</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR TS GUESS 631G G TSONCENOEIGEN.mol</uploadedFileContents> </jmolApplet></jmol>
====== Summary ======
[[Image:WENMIN G CHAIR 631g REOPT SUMMARY.PNG|thumb|center|500px|Reoptimization summary of the chair TS at higher level.]]
====== Output information ======
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001476 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
====== Energy list ======
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
====== File Link ======
Reoptimization: [[File:WENMIN CHAIR TS GUESS 631G G TSONCENOEIGEN.LOG‎]]

Frequency: [[File:WENMIN CHAIR TS GUESS 631G G FREQ.LOG]]

==== Results 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" | -231.619322
| align="center" | -231.466693
| align="center" | -231.461334
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450922
| align="center" | -231.445294
| align="center" | -234.543093
| align="center" | -234.402336
| align="center" | -234.396003
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611703
| 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.<ref name="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" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

 

When comparing the TS energy at higher level (B3LYP/6-31G*) with the one at lower level (HF/3-21G), the difference is not very obvious in hartree unit. But even 0.01 difference in hartree means about 6 kcal/mol difference. This can be confirmed by the second table. The values obtained at B3LYP/6-31G* level agree with the experimental value much better than the ones at HF/3-21G. The activation energy of chair TS is lower than that of boat TS, so we can confirm that the Cope Rearrangement has a chair transition state.

== The Diels Alder Cycloaddition ==
In this section, all calculations are carried out using the '''AM1 semi-empirical''' molecular orbital method. As for the computation of the TS geometry optimization, '''TS (Berny)''', calculate the force constants '''Once''', and additional keyword of '''Opt=NoEigen''' are specified because it's a better approach as shown in the first part.
=== Cis-butadiene ===
A cis-butadiene is drawn and optmized, using the '''AM1 semi-empirical''' molecular orbital method by the GaussView. The followings are the result:
==== Molecule ====
<jmol><jmolApplet> <title>Cis-butadiene molecule</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 1 CISBUTADIENE OPT SEMIPIRICAL AM1.mol</uploadedFileContents> </jmolApplet></jmol>
==== Summary ====
[[Image:WENMIN 1 CISBUTADIENE SUMMARY.PNG|thumb|center|500px|Optimization summary of the cis-butadiene.]]
==== Output information ====
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000330 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
==== HOMO and LUMO ====
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
| [[Image:WENMIN 1 CISBUTADIENE HOMO2.PNG|thumb|center|500px|HOMO MO of cis-butadiene.]] || [[Image:WENMIN 1 CISBUTADIENE LUMO2.PNG|thumb|center|500px|LUMO MO of cis-butadiene.]]
|}
[[Image:1_CISBUTADIENE_HOMOandLUMOnew.png|thumb|center|500px|HOMO & LUMO symmetry of cis-butadiene with respect to yz plane.]]

==== Link file ====
[[File:WENMIN 1 CISBUTADIENE OPT SEMIPIRICAL AM1.LOG]]

=== TS geometry for the prototype reaction ===
[[Image:Mb_da3.jpg|thumb|right|200px|Prototype reaction]]
[[Image:Mb_da4.jpg|thumb|right|200px|Guessing geometry]]
The guessing TS geometry for the prototype reaction is the geometry (a). It is optimized using '''TS (Berny)''', calculate the force constants '''Once''', and additional keyword of '''Opt=NoEigen''', under the '''AM1 semi-empirical''' molecular orbital method by the GaussView. The followings are the result:
==== Molecule ====
<jmol><jmolApplet> <title>Guess TS</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 2 TS OPT FREQ TSBERNY ONCE NOEIGEN.mol</uploadedFileContents> </jmolApplet></jmol>
==== Summary ====
[[Image:WENMIN 2 TS SUMMARY.PNG|thumb|center|500px|Optimization summary of the guess TS.]]
==== Output information ====
Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000080 0.001800 YES
RMS Displacement 0.000026 0.001200 YES
==== Vibration frequencies ====
There's only one imaginary frequency of magnitude 956.19 cm-1, conforming that this geometry is a TS.
[[Image:WENMIN_2_TS_VIBRATION.PNG|thumb|center|500px]]
{| class="wikitable" border="1"
|+ Vibration Frequencies
! Imaginary Frequency !! Lowest Positive Frequency
|-
| [[File:WENMIN 2 TS IMAGINARY VIBRATION.gif]] || [[File:WENMIN 2 TS LOWESTPOSITIVE VIBRATION.gif]]
|}
From the imaginary frequency we can see that the formation of two bonds is synchronous and symmetrical. This confirms that the concerted mechanisms of the reaction. The terminal ends of diene and ethylene are vibrating towards each other (back and forth). A reaction is undergoing between these two molecules. By contrast, in the lowest positive frequency, these two molecules are doing vibration on their own and no interaction whatsoever is happening between them. Another interesting point here is that carbon atoms and hydrogen atoms are vibrating in opposite directions in imaginary frequency, while C and H atoms are vibrating in the same direction in the lowest positive frequency.

==== HOMO & LUMO====
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
| [[Image:WENMIN 2 TS HOMO1.PNG|thumb|center|500px|HOMO MO of the guess TS.]] || [[Image:WENMIN_2_TS_LUMO1.PNG|thumb|center|500px|LUMO MO of the guess TS.]]
|}
[[Image:WENMIN 2 TS HOMOandLUMO_SYMMETRY.png|thumb|center|500px|HOMO & LUMO symmetry of the guess TS. (The isovalue is changed to 0.04 to get rid of the orbital overlap for more obvious symmetry.)]]

==== Bond length ====
{| class="wikitable" border="1"
|-
| [[Image:WENMIN 2 TS partlyformedCC BondLength1.PNG|thumb|center|500px|Bond length of partly formed C8-C11 bond.]] || [[Image:WENMIN 2 TS partlyformedCC BondLength2.PNG|thumb|center|500px|Bond length of partly formed C5-C14 bond.]]
|}
{| class="wikitable" border="1"
|+ Bond length comparison
! C-C sp3-sp3 !! C-C sp2-sp2 !! C-C van der Waals !! C-C TS from calculation
|-
| 1.54Å<ref name=1.54 /> || 1.34Å<ref name=1.33 /> || ~1.7Å<ref name=1.7 /> || 2.12Å
|}
The bond distance in the TS, from calculation, is smaller than the van der Waals radius, but larger than that of both σC-C and πC-C bond. This shows the bond is partly formed into a σC-C bond during the transition state.

==== MO ====
[[Image:WENMIN_2_TS_MO.png|thumb|center|900px|Analysis of Diels Alder reaction.]]
==== Link file ====
[[File:WENMIN 2 TS OPT FREQ TSBERNY ONCE NOEIGEN.LOG]]

=== Regioselectivity of the Diels Alder Reaction ===
[[Image:Bearpark_pic_edit_by_jm906.JPG|thumb|right|200px]]
The reaction between '''1''' (cyclohexa-1,3-diene) and '''2''' (maleic anhydride) gives either the endo adduct primarily. This reaction is kinetically controlled so the exo TS should have higher energy than the endo TS.
Both the exo and the endo TS are optimized using '''TS (Berny)''', calculate the force constants '''Once''', and additional keyword of '''Opt=NoEigen''', under the '''AM1 semi-empirical''' molecular orbital method by the GaussView.
==== Exo TS ====
<jmol><jmolApplet> <title>Exo TS</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 3 DIELS ALDER TS EXO.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN 3 DIELS ALDER TS EXO SUMMARY.PNG|thumb|center|500px|Optimization summary of the exo TS.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000062 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001361 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
===== Vibration frequencies =====
There's only one imaginary frequency of magnitude 812.38 cm-1, conforming that this geometry is a TS.
[[Image:WENMIN 3 TS EXO VIBRATION.PNG|thumb|center|500px]]
{| class="wikitable" border="1"
|+ Vibration Frequencies
! Imaginary Frequency !! Lowest Positive Frequency
|-
| [[File:WENMIN 3 EXO IMAGINARY.gif]] || [[File:WENMIN 3 EXO LOWESTPOSITIVE.gif]]
|}
As discussed in Section 2.2.4.

===== HOMO & LUMO =====
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
| [[Image:WENMIN 3 DIELS ALDER TS EXO HOMO.PNG|thumb|center|600px|HOMO MO of the exo TS.]] || [[Image:WENMIN EXO LUMO.PNG|thumb|center|400px|LUMO MO of the exo TS.]]
|}

===== Link file =====
[[File:WENMIN 3 DIELS ALDER TS EXO.LOG]]
==== Endo TS ====
===== Molecule =====
<jmol><jmolApplet> <title>Endo TS</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 3 DIELS ALDER TS ENDO.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN 3 DIELS ALDER TS ENDO SUMMARY.PNG|thumb|center|500px|Optimization summary of the endo TS.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000757 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
===== Vibration frequencies =====
There's only one imaginary frequency of magnitude 806.22 cm-1, conforming that this geometry is a TS.
[[Image:WENMIN 3 TS ENDO VIBRATION.PNG|thumb|center|500px]]
{| class="wikitable" border="1"
|+ Vibration Frequencies
! Imaginary Frequency !! Lowest Positive Frequency
|-
| [[File:WENMIN 3 ENDO IMAGINARY.gif]] || [[File:WENMIN 3 ENDO LOWESTPOSITIVE.gif]]
|}
As discussed in Section 2.2.4.

===== HOMO & LUMO =====
{| class="wikitable" border="1"
! HOMO !! LUMO
|-
| [[Image:WENMIN 3 DIELS ALDER TS ENDO HOMO.PNG|thumb|center|600px|HOMO MO of the endo TS.]] || [[Image:WENMIN ENDO LUMO.PNG|thumb|center|350px|LUMO MO of the endo TS.]]
|}

===== Link file =====
[[File:WENMIN 3 DIELS ALDER TS ENDO.LOG]]

==== Explanation ====
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!DON'T FORGET!
==== Comparison ====
{| class="wikitable" border="1"
|+ Vibration Frequencies
! Exo !! Endo
|-
| [[File:WENMIN 3 DIELS ALDER EXO VIBRATION.gif]] || [[File:WENMIN 3 DIELS ALDER ENDO VIBRATION.gif]]
|}

{| class="wikitable" border="1"
|+ Energy
! Exo !! Endo
|-
| -0.05041980 a.u. || -0.05150478 a.u.
|}
Energy difference ΔE = (-0.05041980) - (-0.05150478) = 1.08498*10-3 a.u. = 0.6808 kcal/mol

Endo geometry has lower energy level and thus it is favored.

{| class="wikitable" border="1"
|+ C-C bond
! Exo !! Endo
|-
| [[Image:WENMIN 3 TS EXO partlyformedCC BondLength.PNG|thumb|500px|Bond distance of partly formed σC-C bond in exo form.]] || [[Image:WENMIN 3 TS ENDO partlyformedCC BondLength.PNG|thumb|500px|Bond distance of partly formed σC-C bond in endo form.]]
|-
| cell || cell
|}
The difference of partly formed C-C bond length in exo form and endo form is very small. The endo form has a little bit shorter length than the exo one since the endo form is the more stable.

{| class="wikitable" border="1"
|+ C-C space
! Exo !! Endo
|-
| [[File:WENMIN SPACE EXO.PNG]] || [[File:WENMIN SPACE ENDO.PNG]]
|}
It's shown in the table above that the C-C space in exo TS is larger than the one in endo TS. This confirms that the endo form suffers more steric hindrance than the exo one. However, the difference between them is very small. This is due to the secondary orbital interaction in endo form that pulls carbonyl groups towards the diene, making the C-C space shorter than it should be. This is the result of secondary orbital interaction versus repulsion.

== References ==

<references>
<ref name=" Appendix">Module 3: Transition states and reactivity. [[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3]]</ref>
<ref name="reference">Module 3: Transition states and reactivity. [[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3]]</ref>
<ref name="Expt">Module 3: Transition states and reactivity. [[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3]]</ref>
<ref name="1.54">1986 J. Phys. C: Solid State Phys. 19 4613 </ref>

<ref name="1.33">1986 J. Phys. C: Solid State Phys. 19 4613 </ref>

<ref name="1.7">Dr. Henry Zrepa, Conformational Analysis Lecture Notes [[http://www.ch.ic.ac.uk/local/organic/conf/]]</ref>

</references>

File:WENMIN 3 TS ENDO partlyformedCC BondLength.PNG

2012-11-02T15:58:55Z

Wx610:

2012-11-02T15:26:46Z

2012-11-02T04:53:23Z

Wx610:

File:WENMIN 3 TS EXO orientationCC2 BondLength.PNG

2012-11-02T04:53:23Z

Wx610:

File:WENMIN 3 TS ENDO orientationCC BondLength.PNG

2012-11-02T04:53:23Z

Wx610:

2012-11-01T23:18:08Z

Wx610: /* Vibration frequencies */

== The Cope Rearrangement ==
=== Optimizing the Reactants and Products ===
==== 1,5-hexadiene with an "anti" linkage ====
The "anti" 1,5-hexadiene was optimized at the '''HF/3-21G''' level of theory with memory limit of '''250MB'''. The followings are the summary, symmetry group and molecule structure of the structure:
===== Molecule =====
<jmol><jmolApplet> <title>"Anti" 1,5-hexadiene molecule</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 15 HEXADIENE ANTI.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN 15 HEXADIENE ANTI OPT SUMMARY byCOMPUTER.PNG|thumb|center|500px|Optimization summary of the "anti" 1,5-hexadiene.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000060 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000442 0.001800 YES
RMS Displacement 0.000171 0.001200 YES
===== Symmetry group =====
[[Image:WENMIN 15 HEXADIENE ANTI OPT SYMMERTRY.PNG|thumb|center|500px|Symmetry of the "anti" 1,5-hexadiene.]]
===== File Link =====
[[File:WENMIN 15 HEXADIENE ANTI.LOG]]

==== 1,5-hexadiene with an "gauche" linkage ====
The "gauche" form of 1,5-hexadiene should have lower energy than the "anti" one.
The "gauche" 1,5-hexadiene was optimized at the '''HF/3-21G''' level of theory with memory limit of '''250MB'''. The followings are the summary and symmetry of the structure:
===== Molecule =====
<jmol><jmolApplet> <title>"Gauche" 1,5-hexadiene molecule</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN Log 64127(15 HEXADIENE GAUCHE).mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN 15 HEXADIENE GAUCHE OPT SUMMARY.PNG|thumb|center|500px|Optimization summary of the "gauche" 1,5-hexadiene.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000174 0.001800 YES
RMS Displacement 0.000055 0.001200 YES
===== Symmetry group =====
[[Image:WENMIN 15 HEXADIENE GAUCHE OPT SYMMERTRY.PNG|thumb|center|500px|Symmetry of the "gauche" 1,5-hexadiene.]]
===== File Link =====
[[File:WENMIN Log 64127(15 HEXADIENE GAUCHE).log]]

==== Lowest energy conformation ====
The lowest energy conformation should be the gauche3 form (shown in the Appendix 1<ref name=Appendix />). This form is drawn and optimized at the '''HF/3-21G''' level with memory limit of '''250MB'''. The followings are the results:
===== Molecule =====
<jmol><jmolApplet> <title>1,5-hexadiene molecule with lowest energy</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 15 HEXADIENE GAUCHE 3.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN 15 HEXADIENE GAUCHE 3 SUMMARY.PNG|thumb|center|500px|Optimization summary of the 1,5-hexadiene with lowest energy.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001316 0.001800 YES
RMS Displacement 0.000491 0.001200 YES
===== Symmetry group =====
[[Image:WENMIN_15_HEXADIENE_GAUCHE_3_SYMMETRY.PNG|thumb|center|500px|Symmetry of the 1,5-hexadiene with lowest energy.]]
===== File Link =====
[[File:WENMIN_15_HEXADIENE_GAUCHE_3.LOG]]

==== Structure table ====
Structures and energies are compared with the reference<ref name="reference" />, conformers are identified with specific names.
 

{| border="1" cellpadding="5"
|- align="center"
| width="150" | '''Conformer'''
| width="150" | '''Structure'''
| width="100" | '''Point Group'''
| width="200" | '''Energy/Hartrees HF/3-21G'''
|- align="center"
| Section 1.1.2: ''gauche2''
|
[[Image:WENMIN 15 HEXADIENE GAUCHE OPT MOLECULE.PNG|150px]]
| C2
| -231.69166702
|- align="center"
| Section 1.1.3: ''gauche3''
|
[[Image:WENMIN_15_HEXADIENE_GAUCHE_3_MOLECULE.PNG‎|150px]]
| C1
| -231.69266120
|- align="center"
| Section 1.1.1: ''anti2''
|
[[Image:WENMIN 15 HEXADIENE ANTI MOLECULE.PNG|150px]]
| Ci
| -231.69253528
|- align="center"
|}

 

From the table shown above, we get that gauche3 conformation has the lowest energy, followed by anti2 conformation. The gauche2 conformation has the highest energy here.

We usually have the impression that anti2 conformation should be lowest in energy level for allyl groups. This is mainly because, for small allyl molecules, the anti-periplanar form has the maximizing σC-H/σ*C-H and/or σC-C/σ*C-C conjugation. In addition, the app form relieves the torsional strain. However, as the allyl molecule number increases, gauche form becomes promoted. This is due to the longer distances favoring van der Waals (dispersion) interaction by folding chain back upon itself. In this case, alkene group results in fewer H groups on the sp2 carbon and some bond angles are wider. This leads to reduce hindrance and avoid the H...H contacts of smaller than 2.1Å at which point hydrogen becomes repulsive. What's more, better overlap of πC=C/σ*C=C results in larger stabilizing energy.

==== Reoptimization of "anti2" conformation of 1,5-hexadiene ====
The "anti2" conformation is reoptimized at the '''B3LYP/6-31G(d)''' level. The followings are the results:
===== Molecule =====
<jmol><jmolApplet> <title>"Anti2" 1,5-hexadiene molecule</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 15 HEXADIENE ANTI REOPT.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN_15_HEXADIENE_ANTI_REOPT_SUMMARY.PNG|thumb|center|500px|Reoptimization summary of the "anti2" 1,5-hexadiene at higher level.]]
===== Output information =====
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
===== Symmetry group =====
[[Image:WENMIN 15 HEXADIENE ANTI REOPT SYMMETRY.PNG|thumb|center|500px|Symmetry of the "anti2" 1,5-hexadiene at higher level.]]
The symmetry group changes to C2h at the '''B3LYP/6-31G(d)''' level from Ci at the '''HF/3-21G''' level.
===== File Link =====
[[File:WENMIN_15_HEXADIENE_ANTI_REOPT.LOG‎]]

==== Frequency of "anti2" conformation of 1,5-hexadiene ====
The frequency of the "anti2" conformation is calculated at the '''B3LYP/6-31G(d)''' level. The followings are the results:
===== Summary =====
[[Image:WENMIN 15 HEXADIENE ANTI FREQ SUMMARY.PNG|thumb|center|500px|Frequency summary of the "anti2" 1,5-hexadiene at higher level.]]
===== Frequencies =====
All is real frequencies, no imaginary ones.
[[Image:WENMIN_15_HEXADIENE_ANTI_FREQ_VIBRATION.PNG|thumb|center|300px]]
===== Energy lists =====
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
===== IR =====
[[Image:WENMIN 15 HEXADIENE ANTI FREQ IR.PNG|thumb|center|1000px|IR spectrum of the "anti2" 1,5-hexadiene at higher level.]]
===== File Link =====
[[File:WENMIN 15 HEXADIENE ANTI FREQ.LOG]]

=== Optimizing the "Chair" and "Boat" Transition ===
==== Allyl fragment optimization ====
The allyl fragment (CH2CHCH2) is optimized at the '''HF/3-31G''' level of theory. The followings are the results:
===== Molecule =====
<jmol><jmolApplet> <title>Allyl fragment</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR OPT 321G.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN A ALLYL OPT 321G SUMMARY.PNG|thumb|center|500px|Optimization summary of the allyl fragment.]]
===== Output information =====
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
===== File Link =====
[[File:WENMIN CHAIR OPT 321G.LOG]]

==== Guess TS optimization and frequency ====
The guess TS is made from two allyl fragments with approximately 2.2Å terminal ends. Then the guess TS is calculated under '''Opt+Freq''' job type, with '''Optimization to a TS (Berny)''', calculate the force constants '''Once''', and type '''Opt=NoEigen''' in the Additional keyword box. The followings are the results:
===== Molecule =====
<jmol><jmolApplet> <title>Guess TS</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR TS GUESS.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN B TS GUESS 321G OPT+FREQ SUMMARY.PNG|thumb|center|500px|Optimization summary of the guess TS.]]
===== Output information =====
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
===== Vibration frequencies =====
There's only one imaginary frequency of magnitude 817.98 cm-1, conforming that this geometry is a TS.
[[Image:WENMIN B TS GUESS 321G OPT+FREQ VIBRATION.PNG|thumb|right|500px]]
[[File:WENMIN_B_CHAIR_TS_VIBRATION.gif‎]]

===== Bond distance =====
The bond distances of terminal ends change to about 2.02Å, as shown in the following two diagrams.
[[Image:WENMIN B TS GUESS BondDistance1.PNG|thumb|center|300px]]
[[Image:WENMIN B TS GUESS BondDistance2.PNG|thumb|center|300px]]

===== File Link =====
[[File:WENMIN CHAIR TS GUESS.LOG]]

==== Guess TS optimization using the frozen coordinate method ====
The guess TS is optimized at the '''HF/3-31G''' level of theory, with minimum optimization and the '''Freeze Coordinate''' under '''Bond'''. However, the Gaussian program doesn't respond to the input of 2.20Å fixed bond length. The result obtained does not have 2.20Å terminal ends although they are very close to 2.20Å.
[[Image:WENMIN C TS GUESS 321G OPT FREEZE BondDistance1.PNG|thumb|center|300px]]
[[Image:WENMIN C TS GUESS 321G OPT FREEZE BondDistance2.PNG|thumb|center|300px]]
So I redo the calculation, but this time with fixed 2.20Å terminal ends using "''Modify Bond''" tool. The followings are the results of second trail:
===== Molecule =====
<jmol><jmolApplet> <title>Guess TS with frozen coordinate</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR TS GUESS OPT C NEW FIXED22.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN Summary.PNG|thumb|center|500px|Optimization summary of the guess TS with frozen coordinate.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.001213 0.001800 YES
RMS Displacement 0.000247 0.001200 YES
===== Vibration frequencies =====
There's only one imaginary frequency, conforming that this geometry is a TS.
[[Image:WENMIN C frequency.PNG|thumb|center|500px]]
===== Bond distance =====
This time the length between two terminal ends is exactly 2.20Å, as shown in the following two diagrams.
[[Image:WENMIN Bondlength1.PNG|thumb|center|300px]]
[[Image:WENMIN Bondlength2.PNG|thumb|center|300px]]
===== File Link =====
[[File:WENMIN CHAIR TS GUESS OPT C NEW FIXED22.LOG]]

==== Guess TS optimization using the derivative coordinate method ====
The guess TS obtained from the frozen coordinate method is optimized at the '''HF/3-31G''' level of theory, with minimum optimization and the '''Derivative''' under '''Bond'''. The followings are the results:
===== Molecule =====
<jmol><jmolApplet> <title>Guess TS with derivative coordinate</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR TS GUESS OPT D.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN D TS GUESS 321G OPT FREEZE SUMMARY.PNG|thumb|center|500px|Optimization summary of the guess TS with derivative coordinate.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000032 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001154 0.001800 YES
RMS Displacement 0.000230 0.001200 YES
===== Vibration frequencies =====
There's only one imaginary frequency, conforming that this geometry is a TS. The magnitude of the imaginary frequency is 818.06 cm-1, which is very close to the one got from section 1.2.2.
[[Image:WENMIN D frequency.PNG|thumb|center|500px]]
===== Energy list =====
Sum of electronic and zero-point Energies= -231.466693
Sum of electronic and thermal Energies= -231.461334
Sum of electronic and thermal Enthalpies= -231.460390
Sum of electronic and thermal Free Energies= -231.495198
===== Bond distance =====
The bond distances of terminal ends change to about 2.02Å, as shown in the following two diagrams. When comparing the structures obtained from section 1.2.2 and this section, they are almost identical, both having approximate 2.02Å bond distances between terminal ends. This shows that both methods are good approach to determine the TS, since this is a pretty good "guess" of the transition state structure.
[[Image:WENMIN D TS GUESS 321G OPT FREEZE BondDistance1.PNG|thumb|center|300px]]
[[Image:WENMIN D TS GUESS 321G OPT FREEZE BondDistance2.PNG|thumb|center|300px]]

===== File Link =====
[[File:WENMIN CHAIR TS GUESS OPT D.LOG]]

==== Boat TS optimization using the QST2 method ====
The reactant and product are calculated under '''Opt+Freq''' job type with '''Optimization to a TS (QST2)''', using the structures shown as below.
[[Image:WENMIN E REAC+PROC TS QST2 MOLECULE.PNG|thumb|center|500px]]
The followings are the results:
===== Molecule =====
<jmol><jmolApplet> <title>Reactant</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR REAC TS E NEVER.mol</uploadedFileContents> </jmolApplet></jmol>
<jmol><jmolApplet> <title>Product</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR PROD TS E NEVER.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
NOTE: Ignore the "Chair" under file name. These are boat structures.
[[Image:WENMIN E REAC TS QST2 SUMMARY.PNG|thumb|center|500px|Optimization summary of reactant.]]
[[Image:WENMIN E PROC TS QST2 SUMMARY.PNG|thumb|center|500px|Optimization summary of product.]]
===== Output information =====
Reactant:
Item Value Threshold Converged?
Maximum Force 0.000105 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.001249 0.001800 YES
RMS Displacement 0.000277 0.001200 YES

Product:
Item Value Threshold Converged?
Maximum Force 0.000105 0.000450 YES
RMS Force 0.000022 0.000300 YES
Maximum Displacement 0.001249 0.001800 YES
RMS Displacement 0.000277 0.001200 YES
===== Energy list =====
Reactant:
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445294
Sum of electronic and thermal Enthalpies= -231.444349
Sum of electronic and thermal Free Energies= -231.479768

Product:
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445294
Sum of electronic and thermal Enthalpies= -231.444349
Sum of electronic and thermal Free Energies= -231.479768
===== Vibration frequencies =====
There's only one imaginary frequency, conforming that this geometry is a TS (for reactant and product approach).
[[Image:WENMIN E frequency reactant.PNG|thumb|center|500px|Vibration frequencies of reactant.]]
[[Image:WENMIN E frequency product.PNG|thumb|center|500px|Vibration frequencies of product.]]
Since the structure of reactant and product is exactly the same, all results are the same.
===== File Link =====
Reactant: [[File:WENMIN CHAIR REAC TS E.LOG]]

Product: [[File:WENMIN CHAIR PROD TS E.LOG]]

==== Chair TS IRC ====
The '''IRC''' ('''Intrinsic Reaction Coordinate''') method is used to follow the minimum energy path from a transition structure down its local minimum on a potential energy surface. The optimized chair TS (with derivative bond in this case) is calculated at '''HF/3-21''' level with '''IRC''' under the '''Job Type''' tab. Compute it in the forward direction, calculate the force constants once and change the number of points along the IRC into 50.
===== IRC result =====
[[Image:WENMIN_Irc_movie.gif‎|thumb|center|300px]]
[[Image:WENMIN Ircpath1.PNG‎|thumb|center|500px|Total energy along IRC]]
[[Image:WENMIN Ircpath2.PNG‎|thumb|center|500px|RMS Gradient Norm along IRC]]
44 intermediate geometries are obtained and the last one has the energy of -231.69157861 a.u.
[[Image:WENMIN F CHAIR TS IRC FROM D.PNG|thumb|center|500px]]
===== Options to reach minimum geometry =====
Then three options are tested receptively to get a minimum conformation.

(i) The last point on the IRC is taken to do a minimum optimization and the energy obtained is -231.69166702 a.u, which is lower than -231.69157861 a.u.
[[Image:WENMIN F1 CHAIR TS IRC OPT.PNG|thumb|center|500px]]
(ii) The chair TS is run an IRC again, but this time with 100 points instead of 50. However, the same result is obtained as the original one (50 points), having 44 intermediate geometries with minimum energy of -231.69157861 a.u. (I try to run this with additional note of maxcycles=50, but the result is unchanged.)
[[Image:WENMIN F2 CHAIR TS IRC FROM D 100.PNG|thumb|center|500px]]
(iii) Redo the IRC specifying that compute the force constant at every step. The job is incomplete, resulting only 21 intermediate geometries.
[[Image:WENMIN F3 CHAIR TS IRC FROM D EVERYSTEP.PNG|thumb|center|500px]]
Overall, the step (i) is the only approach actually works, ending up with the conformation of energy -231.69166702 a.u.

===== File link =====
IRC: [[File:WENMIN CHAIR TS IRC F FROM D ALWAYS.LOG]]

Optimization after IRC: [[File:WENMIN CHAIR TS IRC F1 FROM D OPT.LOG]]

Redo IRC with "n=100": [[File:WENMIN CHAIR TS IRC F2 FROM D ALWAYS.LOG]]

Redo IRC with "compute force constants at every step": [[File:WENMIN CHAIR TS IRC F3 FROM D ONCE.LOG]]

==== Boat & Chair TS reoptimization at higher level ====
The chair and boat transition structures are reoptimized using the '''B3LYP/6-31G(d)''' level of theory and carry out the frequency calculations.
===== Boat TS reoptimization at higher level =====
====== Molecule ======
<jmol><jmolApplet> <title>Boat TS molecule</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN_BOAT_TS_REAC_631G_TSONCENOEIGEN.mol</uploadedFileContents> </jmolApplet></jmol>
====== Summary ======
[[Image:WENMIN G BOAT 631G REOPT SUMMARY.PNG|thumb|center|500px|Reoptimization summary of the boat TS at higher level.]]
====== Output information ======
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000016 0.000300 YES
Maximum Displacement 0.001276 0.001800 YES
RMS Displacement 0.000316 0.001200 YES
====== Energy list ======
Sum of electronic and zero-point Energies= -234.402336
Sum of electronic and thermal Energies= -234.396003
Sum of electronic and thermal Enthalpies= -234.395059
Sum of electronic and thermal Free Energies= -234.431745
====== File Link ======
Reoptimization: [[File:WENMIN BOAT TS REAC 631G TSONCENOEIGEN.LOG‎]]

Frequency: [[File:WENMIN BOAT TS REAC 631G FREQ.LOG]]

===== Chair TS reoptimization at higher level =====
====== Molecule ======
<jmol><jmolApplet> <title>Chair TS molecule</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN CHAIR TS GUESS 631G G TSONCENOEIGEN.mol</uploadedFileContents> </jmolApplet></jmol>
====== Summary ======
[[Image:WENMIN G CHAIR 631g REOPT SUMMARY.PNG|thumb|center|500px|Reoptimization summary of the chair TS at higher level.]]
====== Output information ======
Item Value Threshold Converged?
Maximum Force 0.000025 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.001476 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
====== Energy list ======
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814
====== File Link ======
Reoptimization: [[File:WENMIN CHAIR TS GUESS 631G G TSONCENOEIGEN.LOG‎]]

Frequency: [[File:WENMIN CHAIR TS GUESS 631G G FREQ.LOG]]

==== Results 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" | -231.619322
| align="center" | -231.466693
| align="center" | -231.461334
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450922
| align="center" | -231.445294
| align="center" | -234.543093
| align="center" | -234.402336
| align="center" | -234.396003
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611703
| 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.<ref name="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" | 45.71
| align="center" | 44.70
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.97
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

 

When comparing the TS energy at higher level (B3LYP/6-31G*) with the one at lower level (HF/3-21G), the difference is not very obvious in hartree unit. But even 0.01 difference in hartree means about 6 kcal/mol difference. This can be confirmed by the second table. The values obtained at B3LYP/6-31G* level agree with the experimental value much better than the ones at HF/3-21G. The activation energy of chair TS is lower than that of boat TS, so we can confirm that the Cope Rearrangement has a chair transition state.

== The Diels Alder Cycloaddition ==
In this section, all calculations are carried out using the '''AM1 semi-empirical''' molecular orbital method. As for the computation of the TS geometry optimization, '''TS (Berny)''', calculate the force constants '''Once''', and additional keyword of '''Opt=NoEigen''' are specified because it's a better approach as shown in the first part.
=== Cis-butadiene ===
A cis-butadiene is drawn and optmized, using the '''AM1 semi-empirical''' molecular orbital method by the GaussView. The followings are the result:
==== Molecule ====
<jmol><jmolApplet> <title>Cis-butadiene molecule</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 1 CISBUTADIENE OPT SEMIPIRICAL AM1.mol</uploadedFileContents> </jmolApplet></jmol>
==== Summary ====
[[Image:WENMIN 1 CISBUTADIENE SUMMARY.PNG|thumb|center|500px|Optimization summary of the cis-butadiene.]]
==== Output information ====
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000330 0.001800 YES
RMS Displacement 0.000162 0.001200 YES
==== HOMO and LUMO ====
[[Image:WENMIN 1 CISBUTADIENE HOMO2.PNG|thumb|center|500px|HOMO MO of cis-butadiene.]]
[[Image:WENMIN 1 CISBUTADIENE LUMO2.PNG|thumb|center|500px|LUMO MO of cis-butadiene.]]
[[Image:1_CISBUTADIENE_HOMOandLUMOnew.png|thumb|center|500px|HOMO & LUMO symmetry of cis-butadiene with respect to yz plane.]]
[[Image:WENMIN_2_TS_HOMOandLUMO_xyplane.PNG|thumb|center|500px|HOMO & LUMO symmetry of cis-butadiene with respect to xy plane.]]
==== Link file ====
[[File:WENMIN 1 CISBUTADIENE OPT SEMIPIRICAL AM1.LOG]]

=== TS geometry for the prototype reaction ===
[[Image:Mb_da3.jpg|thumb|right|200px|Prototype reaction]]
[[Image:Mb_da4.jpg|thumb|right|200px|Guessing geometry]]
The guessing TS geometry for the prototype reaction is the geometry (a). It is optimized using '''TS (Berny)''', calculate the force constants '''Once''', and additional keyword of '''Opt=NoEigen''', under the '''AM1 semi-empirical''' molecular orbital method by the GaussView. The followings are the result:
==== Molecule ====
<jmol><jmolApplet> <title>Guess TS</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 2 TS OPT FREQ TSBERNY ONCE NOEIGEN.mol</uploadedFileContents> </jmolApplet></jmol>
==== Summary ====
[[Image:WENMIN 2 TS SUMMARY.PNG|thumb|center|500px|Optimization summary of the guess TS.]]
==== Output information ====
Item Value Threshold Converged?
Maximum Force 0.000014 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000080 0.001800 YES
RMS Displacement 0.000026 0.001200 YES
==== Vibration frequencies ====
There's only one imaginary frequency of magnitude 956.19 cm-1, conforming that this geometry is a TS.
[[Image:WENMIN_2_TS_VIBRATION.PNG|thumb|center|500px]]
{| class="wikitable" border="1"
|+ Vibration Frequencies
! Imaginary Frequency !! Lowest Positive Frequency
|-
| [[File:WENMIN 2 TS IMAGINARY VIBRATION.gif]] || [[File:WENMIN 2 TS LOWESTPOSITIVE VIBRATION.gif]]
|}
From the imaginary frequency we can see that the formation of two bonds is synchronous. The terminal ends of diene and ethylene are vibrating towards each other (back and forth). A reaction is undergoing between these two molecules. By contrast, in the lowest positive frequency, these two molecules are doing vibration on their own and no interaction whatsoever is happening between them. Another point here is that carbon atoms and hydrogen atoms are vibrating in opposite directions in imaginary frequency, while C and H atoms are vibrating in the same direction in the lowest positive frequency.
==== HOMO & LUMO====
[[Image:WENMIN 2 TS HOMO1.PNG|thumb|center|500px|HOMO MO of the guess TS.]]
[[Image:WENMIN_2_TS_LUMO1.PNG|thumb|center|500px|LUMO MO of the guess TS.]]
[[Image:WENMIN 2 TS HOMOandLUMO_SYMMETRY.png|thumb|center|500px|HOMO & LUMO symmetry of the guess TS. (The isovalue is changed to 0.04 to get rid of the orbital overlap for more obvious symmetry.)]]
==== Bond length ====
[[Image:WENMIN 2 TS partlyformedCC BondLength1.PNG|thumb|center|500px|Bond length of partly formed C8-C11 bond.]]
[[Image:WENMIN 2 TS partlyformedCC BondLength2.PNG|thumb|center|500px|Bond length of partly formed C5-C14 bond.]]
{| class="wikitable" border="1"
|+ Bond length comparison
! C-C sp3-sp3 !! C-C sp2-sp2 !! C-C van der Waals !! C-C TS from calculation
|-
| 1.54Å<ref name=1.54 /> || 1.34Å<ref name=1.33 /> || 3.2Å<ref name=3.2 /> || 2.12Å
|}
The bond distance in the TS, from calculation, is smaller than the van der Waals radius, but larger than that of both σC-C and πC-C bond. This shows the bond is partly formed into a σC-C bond during the transition state.
==== MO ====
[[Image:WENMIN_2_TS_MO.png|thumb|center|900px|Analysis of Diels Alder reaction.]]
==== Link file ====
[[File:WENMIN 2 TS OPT FREQ TSBERNY ONCE NOEIGEN.LOG]]

=== Regioselectivity of the Diels Alder Reaction ===
[[Image:Bearpark_pic_edit_by_jm906.JPG|thumb|right|200px]]
The reaction between '''1''' (cyclohexa-1,3-diene) and '''2''' (maleic anhydride) gives either the endo adduct primarily. This reaction is kinetically controlled so the exo TS should have higher energy than the endo TS.
Both the exo and the endo TS are optimized using '''TS (Berny)''', calculate the force constants '''Once''', and additional keyword of '''Opt=NoEigen''', under the '''AM1 semi-empirical''' molecular orbital method by the GaussView.
==== Exo TS ====
<jmol><jmolApplet> <title>Exo TS</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 3 DIELS ALDER TS EXO.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN 3 DIELS ALDER TS EXO SUMMARY.PNG|thumb|center|500px|Optimization summary of the exo TS.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000062 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001361 0.001800 YES
RMS Displacement 0.000195 0.001200 YES
===== Vibration frequencies =====
There's only one imaginary frequency of magnitude 812.38 cm-1, conforming that this geometry is a TS.
[[Image:WENMIN 3 TS EXO VIBRATION.PNG|thumb|center|500px]]
{| class="wikitable" border="1"
|+ Vibration Frequencies
! Imaginary Frequency !! Lowest Positive Frequency
|-
| [[File:WENMIN 3 EXO IMAGINARY.gif]] || [[File:WENMIN 3 EXO LOWESTPOSITIVE.gif]]
|}

===== HOMO & LUMO =====
[[Image:WENMIN 3 DIELS ALDER TS EXO HOMO.PNG|thumb|center|500px|HOMO MO of the exo TS.]]
'''LUMO!!!!!!!!!!!!!!!!!!!!!!'''

===== Link file =====
[[File:WENMIN 3 DIELS ALDER TS EXO.LOG]]
==== Endo TS ====
===== Molecule =====
<jmol><jmolApplet> <title>Endo TS</title> <color>black</color> <size>200</size>
<uploadedFileContents>WENMIN 3 DIELS ALDER TS ENDO.mol</uploadedFileContents> </jmolApplet></jmol>
===== Summary =====
[[Image:WENMIN 3 DIELS ALDER TS ENDO SUMMARY.PNG|thumb|center|500px|Optimization summary of the endo TS.]]
===== Output information =====
Item Value Threshold Converged?
Maximum Force 0.000031 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000757 0.001800 YES
RMS Displacement 0.000128 0.001200 YES
===== Vibration frequencies =====
There's only one imaginary frequency of magnitude 806.22 cm-1, conforming that this geometry is a TS.
[[Image:WENMIN 3 TS ENDO VIBRATION.PNG|thumb|center|500px]]
{| class="wikitable" border="1"
|+ Vibration Frequencies
! Imaginary Frequency !! Lowest Positive Frequency
|-
| [[File:WENMIN 3 ENDO IMAGINARY.gif]] || [[File:WENMIN 3 ENDO LOWESTPOSITIVE.gif]]
|}

===== HOMO & LUMO =====
[[Image:WENMIN 3 DIELS ALDER TS ENDO HOMO.PNG|thumb|center|500px|HOMO MO of the endo TS.]]
'''LUMO!!!!!!!!!!!!!!!!!!!!!!!!!'''

===== Link file =====
[[File:WENMIN 3 DIELS ALDER TS ENDO.LOG]]

==== Comparison ====
{| class="wikitable" border="1"
|+ Vibration Frequencies
! Exo !! Endo
|-
| [[File:WENMIN 3 DIELS ALDER EXO VIBRATION.gif]] || [[File:WENMIN 3 DIELS ALDER ENDO VIBRATION.gif]]
|}
{| class="wikitable" border="1"
|+ Energy
! Exo !! Endo !!
|-
| -0.05041980 a.u. || -0.05150478 a.u.
|}
Energy difference ΔE = (-0.05041980) - (-0.05150478) = 1.08498*10-3 a.u. = 0.6808 kcal/mol

== References ==

<references>
<ref name=" Appendix">Module 3: Transition states and reactivity. [[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3]]</ref>
<ref name="reference">Module 3: Transition states and reactivity. [[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3]]</ref>
<ref name="Expt">Module 3: Transition states and reactivity. [[https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3]]</ref>
<ref name="1.54">1986 J. Phys. C: Solid State Phys. 19 4613 </ref>

<ref name="1.33">1986 J. Phys. C: Solid State Phys. 19 4613 </ref>

<ref name="3.2">Dr. Henry Zrepa, Conformational Analysis Lecture Notes [[http://www.ch.ic.ac.uk/local/organic/conf/]]</ref>

</references>