ChemWiki - User contributions [en]

Rep:Mod3:YJY1234

2011-11-11T16:31:29Z

Jy1109:

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-608308.7506 || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by 2.64 kJ/mol.

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || -231.69253528||-234.61170280

|-

|Energy/ kJ mol-1 ||-608308.7506||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles.

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

The boat transition structure is optimized using the QST2 method, which specifies the reactants and products for a reaction in attempt to calculate the transition state.
The DFT-B3LYP/6-31G(d) optmized ''anti2'' 1,5-hexadiene structure was duplicated, labelled and oriented so that they mimic the reactant and product. Then, the first QST2 calculation was run, but this job failed as the starting structures differed too much from the transition state. Therefore, the structure of the starting structures were modified so that they are closer to the boat transition state structure.

'''''Graph 7'' - the modified starting structures'''

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

The QST2 calculation was started again. This time, the transition state structure was successfully located.

'''''Graph 8'' - the boat transition state structure located using the QST2 method'''

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

===The IRC calculation===

Looking at this transition structure, as well as the structure for the chair transition state, it is impossible to predict which conformer will form. However, another method called the Intrinsic Coordinate (IRC) Method allows us to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

To find out the minimum energy path of the reaction, the IRC calculation was run for the chair transition state structure. However, after the calculation, the minimum geometry was not reached yet. The energy of the final structure is -231.68049221 a.u..

To continue minimizing in attempt to reach the minimum geometry, the last point on the IRC was taken to run a minimum minimization using the HF/3-21G level of theory.

Graph 9 - the final structure of the geometry optimization

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

The energy of this structure is -231.69166702 a.u., which is slightly lower than the starting structure. However, this is still not the minimum geometry.

Another attempt to obtain the minimimum geometry was to redo the IRC, specifying that force constants should be calculated at every step. After redoing the IRC, the geometry minimum was obtained.

Graph 10 - the final structure after redoing the IRC

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

The energy of this structure is -231.79116428 a.u.. The RMS gradient norm for the calculation is 0.00001145 a.u., which is less than 0.001 a.u., showing that the optimization is converged.
The first approach was much faster than the second approach, but as the starting structure was not close to the minimum structure to begin with, it was not able to locate the minimum structure. The second approach was more time-consuming, but it successfully calculated the minimum structure.

===Activation energies===

In this section, the activation energies for the reaction via both transition structures were calculated. Firstly, the chair and boat transition structure were reoptimized using the B3LYP/6-31G* level of theory and frequency calculations were carried out.The structures and energies of the optimized structures are compared with the geometry optimized using HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Table 4 - comparing the chair transition structure optimized at two different levels of theory
! Level of theory !! Structure !! Energy/a.u. !! Energy/ kJ mol-1
|-
| HF/3-21G || [[File:Optimized_strcuture_for_b.PNG|300px]] || -231.680492 ||-608277.132
|-
| B3LYP/6-31G* ||[[File:Structure_after_optmiization_in_part_g.PNG|300px]]||-234.563120||-615845.472
|-
|}

The two structures are similar, but the energy optimized using B3LYP/6-31G* level of theory is 7730 kJ mol-1 lower.

{| class="wikitable" border="1"
|+ Table 5 - comparing the boat transition structure optimized at two different levels of theory
! Level of theory !! Structure !! Energy/a.u. !! Energy/ kJ mol-1
|-
| HF/3-21G || [[File:Trans_state_opt_after_modifying_angle.PNG|300px]] || -231.670907 ||-608251.966
|-
| B3LYP/6-31G* ||[[File:Boat_optimisation_g.png|300px]]||-234.6634537||-616108.898
|-
|}

The two structures are similar, but the energy optimized using B3LYP/6-31G* level of theory is 7857 kJ mol-1 lower.

The imaginary frequency of the reoptimized boat transition structure is -532 cm -1, while the imaginary frequency of the reoptimized chair structure is -567 cm-1.

{| class="wikitable" border="1"
|+ Table 6 - Summary of energies for the Ci (''anti 2'') reactant, chair and boat transition state
|-
!colspan="1"|
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
|
| '''Electronic energy/a.u.'''
| '''Sum of electronic and zero-point energies at 0K/a.u.'''
| '''Sum of electronic and thermal energies at 298.15K/a.u. '''
| '''Electronic energy/a.u.'''
| '''Sum of electronic and zero-point energies at 0K/a.u.'''
|'''Sum of electronic and thermal energies at 298.15K/a.u.'''
|-
| '''Chair Transition State'''
| align="center" |-231.680492
| align="center" |-231.527869
| align="center" |-231.522510
| align="center" |-234.563120
| align="center" |-234.421066
| align="center" |-234.415145
|-
| '''Boat Transition State'''
| align="center" |-231.670907
| align="center" |-231.519026
| align="center" |-231.510941
| align="center" |-234.663454
| align="center" |-234.522703
| align="center" |-234.516360
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.592535

| align="center" |-231.599506
| align="center" |-231.752501
| align="center" | -234.611702
| align="center" | -234.49195
| align="center" | -234.461849
|}

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table 7 - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table 8 - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Symmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph 11 - the prototype reaction

[[File:Prototype_reac.png]]

Graph 12 - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table 9 - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph 13 - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table 10 - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph 14 - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated.

{| class="wikitable" border="1"
|+ Table 11 - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph 15 - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table 12 - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation.

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table 13 - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

'''Graph 16 - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride
'''

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table 14 -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table 17 - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_unfreeze_barny_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

'''Graph 17 - the labelled diagram of the ''exo'' transition state after optimization
'''
[[File:Exo_labelled_diagram_for_geometry_analysis.PNG|500px]]

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !!
|-
|C1 and C3, C6 and C5 || 1.39
|-
|C5 and C13 || 1.39
|-
|C3 and C6 || 1.40
|-
| C1 and C8, C10 and C15 || 1.51
|-
|C8 and C10 || 1.56
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40
|-
|C18 and O21, C17 and O20 || 1.20
|-

|}

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table 18 - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table 19 - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_endo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Endo_DFT_optimised_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05238788 || -0.0515048 || -612.68339675
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00272262 || 0.00000811 || 0.00000704
|-align="center"
| '''Dipole moment/ Debye''' || 6.0005 || 6.1660 || 6.1142
|-align="center"
|'''Job CPU time''' || 16 seconds || 3 seconds || 35 minutes 32 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.16 || 2.27
|-align="center"
|'''Imaginary frequency/ cm-1 '''|| - ||-806 || -447
|-
|}

After the optimization, the geometry of the optimized structure is analyzed.

Diagram 17 - the labelled diagram of the ''endo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table 19 - Geometry analysis of the optimized ''endo'' transition state
! Bonds !! Bond lengths/ Å
|-
|C1 and C5, C3 and C7 || 1.39
|-
|C1 and C3 || 1.40
|-
|C5 and C16, C13 and C7 || 1.52
|-
| C1 and C8, C10 and C15 || 1.51
|-
|C13 and C16 || 1.56
|-
|C11 and C20, C9 and C19 ||1.48
|-
|C20 and O21, C19 and O21 || 1.40
|-
|C19 and O22, C20 and O13 || 0.22
|-

|}

The HOMO and LUMO of the optimized ''endo'' transition state was calculated using GaussView.

{| class="wikitable" border="1"
|+ Table 19 - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Endo_HOMO.PNG|300px]] ||[[File:Endo_LUMO.PNG|300px]]
|-
| '''Symmetry''' || Antisymmetric || Antisymmetric
|-
|}

===Secondary orbital overlap effect===

Experimental observation is that the reaction between maleic anhydride and cyclopentadiene gives the ''endo'' adduct faster than they give the ''exo'' adduct even though the latter is more thermodynamically stable.(pp.106). This is because the transition state of the ''endo'' isomer is lower in energy, as show in the table below:
{| class="wikitable" border="1"
|+Table 20 - The energies of the optimized transition states from the DFT-B3LYP/6-31G(d) optimization
! !! ''Exo'' adduct !! ''Endo'' adduct
|-
| Energy/a.u. ||-612.67931095|| -612.68339675

|-

| Energy/kJ mol-1 || -1608589.5309||-1608600.2582

|-
|}

The ''exo'' adduct is more stable than the ''endo'' adduct by 10.7 kJ mol-1. This is due to the presence of secondary overlap of frontier orbitals in the ''endo'' transition state, which is not present in the ''exo'' transition state.

Diagram 18 - the interaction of frontier orbitals in the ''endo'' transition state

[[file:Endo_mechanism.png]]

The dashed lines in the diagram above denote bond-forming interactions, while the dotted lines donate non-bond forming secondary orbital interactions. In the endo transition state, only bond-forming interactions are present:

Diagram 19 - the interaction of frontier orbitals in the ''exo'' transition state

[[File:Exo_mechanism.png]]

The HOMO of both ''endo'' and ''exo'' transition states have nodal planes. However, secondary overlap is hard to confirm from the calculated HOMO diagrams, as they all show a similar degree of overlap. This might be due to the choose of method and basis set which is not accurate enough to be able to illustrate the secondary interactions in the calculated diagram. Hence, another more accurate method should be used to examine the HOMOs of the two transition states.

Examine the shapes of the optimized ''endo'' and ''exo'' transition states, we can see that for the ''exo'' isomer, the maleic anhydride molecule fragment is on the same side as the CH2-CH2 group. This leads to large steric strain in the transition state. For the endo isomer, the maleic anhydride fragment is on the opposite side as the CH2-CH2 group, which avoids the steric strain.

Therefore, the relative energy of the transition states is depend on two factors: the extent of secondary interactions between the frontier orbitals, and the extent of steric strain. The fact that the ''exo'' adduct is more stable shows that the stabilizing effect by the secondary interactions is greater than the destabilizing effect by the steric hindrance.

=Reference=

Rep:Mod3:YJY1234

2011-11-11T16:25:21Z

Jy1109: /* Optimization of the transition state */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-608308.7506 || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by 2.64 kJ/mol.

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || -231.69253528||-234.61170280

|-

|Energy/ kJ mol-1 ||-608308.7506||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles.

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

The boat transition structure is optimized using the QST2 method, which specifies the reactants and products for a reaction in attempt to calculate the transition state.
The DFT-B3LYP/6-31G(d) optmized ''anti2'' 1,5-hexadiene structure was duplicated, labelled and oriented so that they mimic the reactant and product. Then, the first QST2 calculation was run, but this job failed as the starting structures differed too much from the transition state. Therefore, the structure of the starting structures were modified so that they are closer to the boat transition state structure.

'''''Graph 7'' - the modified starting structures'''

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

The QST2 calculation was started again. This time, the transition state structure was successfully located.

'''''Graph 8'' - the boat transition state structure located using the QST2 method'''

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

===The IRC calculation===

Looking at this transition structure, as well as the structure for the chair transition state, it is impossible to predict which conformer will form. However, another method called the Intrinsic Coordinate (IRC) Method allows us to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

To find out the minimum energy path of the reaction, the IRC calculation was run for the chair transition state structure. However, after the calculation, the minimum geometry was not reached yet. The energy of the final structure is -231.68049221 a.u..

To continue minimizing in attempt to reach the minimum geometry, the last point on the IRC was taken to run a minimum minimization using the HF/3-21G level of theory.

Graph 9 - the final structure of the geometry optimization

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

The energy of this structure is -231.69166702 a.u., which is slightly lower than the starting structure. However, this is still not the minimum geometry.

Another attempt to obtain the minimimum geometry was to redo the IRC, specifying that force constants should be calculated at every step. After redoing the IRC, the geometry minimum was obtained.

Graph 10 - the final structure after redoing the IRC

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

The energy of this structure is -231.79116428 a.u.. The RMS gradient norm for the calculation is 0.00001145 a.u., which is less than 0.001 a.u., showing that the optimization is converged.
The first approach was much faster than the second approach, but as the starting structure was not close to the minimum structure to begin with, it was not able to locate the minimum structure. The second approach was more time-consuming, but it successfully calculated the minimum structure.

===Activation energies===

In this section, the activation energies for the reaction via both transition structures were calculated. Firstly, the chair and boat transition structure were reoptimized using the B3LYP/6-31G* level of theory and frequency calculations were carried out.The structures and energies of the optimized structures are compared with the geometry optimized using HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Table 4 - comparing the chair transition structure optimized at two different levels of theory
! Level of theory !! Structure !! Energy/a.u. !! Energy/ kJ mol-1
|-
| HF/3-21G || [[File:Optimized_strcuture_for_b.PNG|300px]] || -231.680492 ||-608277.132
|-
| B3LYP/6-31G* ||[[File:Structure_after_optmiization_in_part_g.PNG|300px]]||-234.563120||-615845.472
|-
|}

The two structures are similar, but the energy optimized using B3LYP/6-31G* level of theory is 7730 kJ mol-1 lower.

{| class="wikitable" border="1"
|+ Table 5 - comparing the boat transition structure optimized at two different levels of theory
! Level of theory !! Structure !! Energy/a.u. !! Energy/ kJ mol-1
|-
| HF/3-21G || [[File:Trans_state_opt_after_modifying_angle.PNG|300px]] || -231.670907 ||-608251.966
|-
| B3LYP/6-31G* ||[[File:Boat_optimisation_g.png|300px]]||-234.6634537||-616108.898
|-
|}

The two structures are similar, but the energy optimized using B3LYP/6-31G* level of theory is 7857 kJ mol-1 lower.

The imaginary frequency of the reoptimized boat transition structure is -532 cm -1, while the imaginary frequency of the reoptimized chair structure is -567 cm-1.

{| class="wikitable" border="1"
|+ Table 6 - Summary of energies for the Ci (''anti 2'') reactant, chair and boat transition state
|-
!colspan="1"|
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
|
| '''Electronic energy/a.u.'''
| '''Sum of electronic and zero-point energies at 0K/a.u.'''
| '''Sum of electronic and thermal energies at 298.15K/a.u. '''
| '''Electronic energy/a.u.'''
| '''Sum of electronic and zero-point energies at 0K/a.u.'''
|'''Sum of electronic and thermal energies at 298.15K/a.u.'''
|-
| '''Chair Transition State'''
| align="center" |-231.680492
| align="center" |-231.527869
| align="center" |-231.522510
| align="center" |-234.563120
| align="center" |-234.421066
| align="center" |-234.415145
|-
| '''Boat Transition State'''
| align="center" |-231.670907
| align="center" |-231.519026
| align="center" |-231.510941
| align="center" |-234.663454
| align="center" |-234.522703
| align="center" |-234.516360
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.592535

| align="center" |-231.599506
| align="center" |-231.752501
| align="center" | -234.611702
| align="center" | -234.49195
| align="center" | -234.461849
|}

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table 7 - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table 8 - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Symmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph 11 - the prototype reaction

[[File:Prototype_reac.png]]

Graph 12 - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table 9 - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph 13 - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table 10 - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph 14 - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated.

{| class="wikitable" border="1"
|+ Table 11 - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table 12 - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation.

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_unfreeze_barny_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

d===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_endo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Endo_DFT_optimised_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05238788 || -0.0515048 || -612.68339675
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00272262 || 0.00000811 || 0.00000704
|-align="center"
| '''Dipole moment/ Debye''' || 6.0005 || 6.1660 || 6.1142
|-align="center"
|'''Job CPU time''' || 16 seconds || 3 seconds || 35 minutes 32 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.16 || 2.27
|-align="center"
|'''Imaginary frequency/ cm-1 '''|| - ||-806 || -447
|-
|}

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''endo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''endo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C5, C3 and C7 || 1.39 ||
|-
|C1 and C3 || 1.40||
|-
|C5 and C16, C13 and C7 || 1.52||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C13 and C16 || 1.56||
|-
|C11 and C20, C9 and C19 ||1.48 ||
|-
|C20 and O21, C19 and O21 || 1.40||
|-
|C19 and O22, C20 and O13 || 0.22 ||
|-

|}

'''Literature value!'''

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
'''

The HOMO and LUMO of the optimized ''endo'' transition state was calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Endo_HOMO.PNG|300px]] ||[[File:Endo_LUMO.PNG|300px]]
|-
| '''Symmetry''' || Antisymmetric || Antisymmetric
|-
|}

===Secondary orbital overlap effect===

Experimental observation is that the reaction between maleic anhydride and cyclopentadiene gives the ''endo'' adduct faster than they give the ''exo'' adduct even though the latter is more thermodynamically stable.(pp.106). This is because the transition state of the ''endo'' isomer is lower in energy, as show in the table below:
{| class="wikitable" border="1"
|+Table ? - The energies of the optimized transition states from the DFT-B3LYP/6-31G(d) optimization
! !! ''Exo'' adduct !! ''Endo'' adduct
|-
| Energy/a.u. ||-612.67931095|| -612.68339675

|-

| Energy/kJ mol-1 || -1608589.5309||-1608600.2582

|-
|}

The ''exo'' adduct is more stable than the ''endo'' adduct by 10.7 kJ mol-1. This is due to the presence of secondary overlap of frontier orbitals in the ''endo'' transition state, which is not present in the ''exo'' transition state.

Diagram ? - the interaction of frontier orbitals in the ''endo'' transition state

[[file:Endo_mechanism.png]]

The dashed lines in the diagram above denote bond-forming interactions, while the dotted lines donate non-bond forming secondary orbital interactions. In the endo transition state, only bond-forming interactions are present:

Diagram ? - the interaction of frontier orbitals in the ''exo'' transition state

[[File:Exo_mechanism.png]]

The HOMO of both ''endo'' and ''exo'' transition states have nodal planes. However, secondary overlap is hard to confirm from the calculated HOMO diagrams, as they all show a similar degree of overlap. This might be due to the choose of method and basis set which is not accurate enough to be able to illustrate the secondary interactions in the calculated diagram. Hence, another more accurate method should be used to examine the HOMOs of the two transition states.

Examine the shapes of the optimized ''endo'' and ''exo'' transition states, we can see that for the ''exo'' isomer, the maleic anhydride molecule fragment is on the same side as the CH2-CH2 group. This leads to large steric strain in the transition state. For the endo isomer, the maleic anhydride fragment is on the opposite side as the CH2-CH2 group, which avoids the steric strain.

Therefore, the relative energy of the transition states is depend on two factors: the extent of secondary interactions between the frontier orbitals, and the extent of steric strain. The fact that the ''exo'' adduct is more stable shows that the stabilizing effect by the secondary interactions is greater than the destabilizing effect by the steric hindrance.

=Reference=

Rep:Mod3:YJY1234

2011-11-11T16:21:41Z

Jy1109: /* Optimization and MO analysis of cis butadiene */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-608308.7506 || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by 2.64 kJ/mol.

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || -231.69253528||-234.61170280

|-

|Energy/ kJ mol-1 ||-608308.7506||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles.

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

The boat transition structure is optimized using the QST2 method, which specifies the reactants and products for a reaction in attempt to calculate the transition state.
The DFT-B3LYP/6-31G(d) optmized ''anti2'' 1,5-hexadiene structure was duplicated, labelled and oriented so that they mimic the reactant and product. Then, the first QST2 calculation was run, but this job failed as the starting structures differed too much from the transition state. Therefore, the structure of the starting structures were modified so that they are closer to the boat transition state structure.

'''''Graph 7'' - the modified starting structures'''

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

The QST2 calculation was started again. This time, the transition state structure was successfully located.

'''''Graph 8'' - the boat transition state structure located using the QST2 method'''

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

===The IRC calculation===

Looking at this transition structure, as well as the structure for the chair transition state, it is impossible to predict which conformer will form. However, another method called the Intrinsic Coordinate (IRC) Method allows us to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

To find out the minimum energy path of the reaction, the IRC calculation was run for the chair transition state structure. However, after the calculation, the minimum geometry was not reached yet. The energy of the final structure is -231.68049221 a.u..

To continue minimizing in attempt to reach the minimum geometry, the last point on the IRC was taken to run a minimum minimization using the HF/3-21G level of theory.

Graph 9 - the final structure of the geometry optimization

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

The energy of this structure is -231.69166702 a.u., which is slightly lower than the starting structure. However, this is still not the minimum geometry.

Another attempt to obtain the minimimum geometry was to redo the IRC, specifying that force constants should be calculated at every step. After redoing the IRC, the geometry minimum was obtained.

Graph 10 - the final structure after redoing the IRC

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

The energy of this structure is -231.79116428 a.u.. The RMS gradient norm for the calculation is 0.00001145 a.u., which is less than 0.001 a.u., showing that the optimization is converged.
The first approach was much faster than the second approach, but as the starting structure was not close to the minimum structure to begin with, it was not able to locate the minimum structure. The second approach was more time-consuming, but it successfully calculated the minimum structure.

===Activation energies===

In this section, the activation energies for the reaction via both transition structures were calculated. Firstly, the chair and boat transition structure were reoptimized using the B3LYP/6-31G* level of theory and frequency calculations were carried out.The structures and energies of the optimized structures are compared with the geometry optimized using HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Table 4 - comparing the chair transition structure optimized at two different levels of theory
! Level of theory !! Structure !! Energy/a.u. !! Energy/ kJ mol-1
|-
| HF/3-21G || [[File:Optimized_strcuture_for_b.PNG|300px]] || -231.680492 ||-608277.132
|-
| B3LYP/6-31G* ||[[File:Structure_after_optmiization_in_part_g.PNG|300px]]||-234.563120||-615845.472
|-
|}

The two structures are similar, but the energy optimized using B3LYP/6-31G* level of theory is 7730 kJ mol-1 lower.

{| class="wikitable" border="1"
|+ Table 5 - comparing the boat transition structure optimized at two different levels of theory
! Level of theory !! Structure !! Energy/a.u. !! Energy/ kJ mol-1
|-
| HF/3-21G || [[File:Trans_state_opt_after_modifying_angle.PNG|300px]] || -231.670907 ||-608251.966
|-
| B3LYP/6-31G* ||[[File:Boat_optimisation_g.png|300px]]||-234.6634537||-616108.898
|-
|}

The two structures are similar, but the energy optimized using B3LYP/6-31G* level of theory is 7857 kJ mol-1 lower.

The imaginary frequency of the reoptimized boat transition structure is -532 cm -1, while the imaginary frequency of the reoptimized chair structure is -567 cm-1.

{| class="wikitable" border="1"
|+ Table 6 - Summary of energies for the Ci (''anti 2'') reactant, chair and boat transition state
|-
!colspan="1"|
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
|
| '''Electronic energy/a.u.'''
| '''Sum of electronic and zero-point energies at 0K/a.u.'''
| '''Sum of electronic and thermal energies at 298.15K/a.u. '''
| '''Electronic energy/a.u.'''
| '''Sum of electronic and zero-point energies at 0K/a.u.'''
|'''Sum of electronic and thermal energies at 298.15K/a.u.'''
|-
| '''Chair Transition State'''
| align="center" |-231.680492
| align="center" |-231.527869
| align="center" |-231.522510
| align="center" |-234.563120
| align="center" |-234.421066
| align="center" |-234.415145
|-
| '''Boat Transition State'''
| align="center" |-231.670907
| align="center" |-231.519026
| align="center" |-231.510941
| align="center" |-234.663454
| align="center" |-234.522703
| align="center" |-234.516360
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.592535

| align="center" |-231.599506
| align="center" |-231.752501
| align="center" | -234.611702
| align="center" | -234.49195
| align="center" | -234.461849
|}

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table 7 - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table 8 - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Symmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_unfreeze_barny_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

d===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_endo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Endo_DFT_optimised_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05238788 || -0.0515048 || -612.68339675
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00272262 || 0.00000811 || 0.00000704
|-align="center"
| '''Dipole moment/ Debye''' || 6.0005 || 6.1660 || 6.1142
|-align="center"
|'''Job CPU time''' || 16 seconds || 3 seconds || 35 minutes 32 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.16 || 2.27
|-align="center"
|'''Imaginary frequency/ cm-1 '''|| - ||-806 || -447
|-
|}

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''endo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''endo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C5, C3 and C7 || 1.39 ||
|-
|C1 and C3 || 1.40||
|-
|C5 and C16, C13 and C7 || 1.52||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C13 and C16 || 1.56||
|-
|C11 and C20, C9 and C19 ||1.48 ||
|-
|C20 and O21, C19 and O21 || 1.40||
|-
|C19 and O22, C20 and O13 || 0.22 ||
|-

|}

'''Literature value!'''

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
'''

The HOMO and LUMO of the optimized ''endo'' transition state was calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Endo_HOMO.PNG|300px]] ||[[File:Endo_LUMO.PNG|300px]]
|-
| '''Symmetry''' || Antisymmetric || Antisymmetric
|-
|}

===Secondary orbital overlap effect===

Experimental observation is that the reaction between maleic anhydride and cyclopentadiene gives the ''endo'' adduct faster than they give the ''exo'' adduct even though the latter is more thermodynamically stable.(pp.106). This is because the transition state of the ''endo'' isomer is lower in energy, as show in the table below:
{| class="wikitable" border="1"
|+Table ? - The energies of the optimized transition states from the DFT-B3LYP/6-31G(d) optimization
! !! ''Exo'' adduct !! ''Endo'' adduct
|-
| Energy/a.u. ||-612.67931095|| -612.68339675

|-

| Energy/kJ mol-1 || -1608589.5309||-1608600.2582

|-
|}

The ''exo'' adduct is more stable than the ''endo'' adduct by 10.7 kJ mol-1. This is due to the presence of secondary overlap of frontier orbitals in the ''endo'' transition state, which is not present in the ''exo'' transition state.

Diagram ? - the interaction of frontier orbitals in the ''endo'' transition state

[[file:Endo_mechanism.png]]

The dashed lines in the diagram above denote bond-forming interactions, while the dotted lines donate non-bond forming secondary orbital interactions. In the endo transition state, only bond-forming interactions are present:

Diagram ? - the interaction of frontier orbitals in the ''exo'' transition state

[[File:Exo_mechanism.png]]

The HOMO of both ''endo'' and ''exo'' transition states have nodal planes. However, secondary overlap is hard to confirm from the calculated HOMO diagrams, as they all show a similar degree of overlap. This might be due to the choose of method and basis set which is not accurate enough to be able to illustrate the secondary interactions in the calculated diagram. Hence, another more accurate method should be used to examine the HOMOs of the two transition states.

Examine the shapes of the optimized ''endo'' and ''exo'' transition states, we can see that for the ''exo'' isomer, the maleic anhydride molecule fragment is on the same side as the CH2-CH2 group. This leads to large steric strain in the transition state. For the endo isomer, the maleic anhydride fragment is on the opposite side as the CH2-CH2 group, which avoids the steric strain.

Therefore, the relative energy of the transition states is depend on two factors: the extent of secondary interactions between the frontier orbitals, and the extent of steric strain. The fact that the ''exo'' adduct is more stable shows that the stabilizing effect by the secondary interactions is greater than the destabilizing effect by the steric hindrance.

=Reference=

Rep:Mod3:YJY1234

2011-11-11T16:19:46Z

Jy1109: /* The Cope Rearrangement Tutorial */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-608308.7506 || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by 2.64 kJ/mol.

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || -231.69253528||-234.61170280

|-

|Energy/ kJ mol-1 ||-608308.7506||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles.

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

The boat transition structure is optimized using the QST2 method, which specifies the reactants and products for a reaction in attempt to calculate the transition state.
The DFT-B3LYP/6-31G(d) optmized ''anti2'' 1,5-hexadiene structure was duplicated, labelled and oriented so that they mimic the reactant and product. Then, the first QST2 calculation was run, but this job failed as the starting structures differed too much from the transition state. Therefore, the structure of the starting structures were modified so that they are closer to the boat transition state structure.

'''''Graph 7'' - the modified starting structures'''

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

The QST2 calculation was started again. This time, the transition state structure was successfully located.

'''''Graph 8'' - the boat transition state structure located using the QST2 method'''

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

===The IRC calculation===

Looking at this transition structure, as well as the structure for the chair transition state, it is impossible to predict which conformer will form. However, another method called the Intrinsic Coordinate (IRC) Method allows us to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

To find out the minimum energy path of the reaction, the IRC calculation was run for the chair transition state structure. However, after the calculation, the minimum geometry was not reached yet. The energy of the final structure is -231.68049221 a.u..

To continue minimizing in attempt to reach the minimum geometry, the last point on the IRC was taken to run a minimum minimization using the HF/3-21G level of theory.

Graph 9 - the final structure of the geometry optimization

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

The energy of this structure is -231.69166702 a.u., which is slightly lower than the starting structure. However, this is still not the minimum geometry.

Another attempt to obtain the minimimum geometry was to redo the IRC, specifying that force constants should be calculated at every step. After redoing the IRC, the geometry minimum was obtained.

Graph 10 - the final structure after redoing the IRC

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

The energy of this structure is -231.79116428 a.u.. The RMS gradient norm for the calculation is 0.00001145 a.u., which is less than 0.001 a.u., showing that the optimization is converged.
The first approach was much faster than the second approach, but as the starting structure was not close to the minimum structure to begin with, it was not able to locate the minimum structure. The second approach was more time-consuming, but it successfully calculated the minimum structure.

===Activation energies===

In this section, the activation energies for the reaction via both transition structures were calculated. Firstly, the chair and boat transition structure were reoptimized using the B3LYP/6-31G* level of theory and frequency calculations were carried out.The structures and energies of the optimized structures are compared with the geometry optimized using HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Table 4 - comparing the chair transition structure optimized at two different levels of theory
! Level of theory !! Structure !! Energy/a.u. !! Energy/ kJ mol-1
|-
| HF/3-21G || [[File:Optimized_strcuture_for_b.PNG|300px]] || -231.680492 ||-608277.132
|-
| B3LYP/6-31G* ||[[File:Structure_after_optmiization_in_part_g.PNG|300px]]||-234.563120||-615845.472
|-
|}

The two structures are similar, but the energy optimized using B3LYP/6-31G* level of theory is 7730 kJ mol-1 lower.

{| class="wikitable" border="1"
|+ Table 5 - comparing the boat transition structure optimized at two different levels of theory
! Level of theory !! Structure !! Energy/a.u. !! Energy/ kJ mol-1
|-
| HF/3-21G || [[File:Trans_state_opt_after_modifying_angle.PNG|300px]] || -231.670907 ||-608251.966
|-
| B3LYP/6-31G* ||[[File:Boat_optimisation_g.png|300px]]||-234.6634537||-616108.898
|-
|}

The two structures are similar, but the energy optimized using B3LYP/6-31G* level of theory is 7857 kJ mol-1 lower.

The imaginary frequency of the reoptimized boat transition structure is -532 cm -1, while the imaginary frequency of the reoptimized chair structure is -567 cm-1.

{| class="wikitable" border="1"
|+ Table 6 - Summary of energies for the Ci (''anti 2'') reactant, chair and boat transition state
|-
!colspan="1"|
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
|
| '''Electronic energy/a.u.'''
| '''Sum of electronic and zero-point energies at 0K/a.u.'''
| '''Sum of electronic and thermal energies at 298.15K/a.u. '''
| '''Electronic energy/a.u.'''
| '''Sum of electronic and zero-point energies at 0K/a.u.'''
|'''Sum of electronic and thermal energies at 298.15K/a.u.'''
|-
| '''Chair Transition State'''
| align="center" |-231.680492
| align="center" |-231.527869
| align="center" |-231.522510
| align="center" |-234.563120
| align="center" |-234.421066
| align="center" |-234.415145
|-
| '''Boat Transition State'''
| align="center" |-231.670907
| align="center" |-231.519026
| align="center" |-231.510941
| align="center" |-234.663454
| align="center" |-234.522703
| align="center" |-234.516360
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.592535

| align="center" |-231.599506
| align="center" |-231.752501
| align="center" | -234.611702
| align="center" | -234.49195
| align="center" | -234.461849
|}

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_unfreeze_barny_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

d===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_endo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Endo_DFT_optimised_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05238788 || -0.0515048 || -612.68339675
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00272262 || 0.00000811 || 0.00000704
|-align="center"
| '''Dipole moment/ Debye''' || 6.0005 || 6.1660 || 6.1142
|-align="center"
|'''Job CPU time''' || 16 seconds || 3 seconds || 35 minutes 32 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.16 || 2.27
|-align="center"
|'''Imaginary frequency/ cm-1 '''|| - ||-806 || -447
|-
|}

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''endo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''endo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C5, C3 and C7 || 1.39 ||
|-
|C1 and C3 || 1.40||
|-
|C5 and C16, C13 and C7 || 1.52||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C13 and C16 || 1.56||
|-
|C11 and C20, C9 and C19 ||1.48 ||
|-
|C20 and O21, C19 and O21 || 1.40||
|-
|C19 and O22, C20 and O13 || 0.22 ||
|-

|}

'''Literature value!'''

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
'''

The HOMO and LUMO of the optimized ''endo'' transition state was calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Endo_HOMO.PNG|300px]] ||[[File:Endo_LUMO.PNG|300px]]
|-
| '''Symmetry''' || Antisymmetric || Antisymmetric
|-
|}

===Secondary orbital overlap effect===

Experimental observation is that the reaction between maleic anhydride and cyclopentadiene gives the ''endo'' adduct faster than they give the ''exo'' adduct even though the latter is more thermodynamically stable.(pp.106). This is because the transition state of the ''endo'' isomer is lower in energy, as show in the table below:
{| class="wikitable" border="1"
|+Table ? - The energies of the optimized transition states from the DFT-B3LYP/6-31G(d) optimization
! !! ''Exo'' adduct !! ''Endo'' adduct
|-
| Energy/a.u. ||-612.67931095|| -612.68339675

|-

| Energy/kJ mol-1 || -1608589.5309||-1608600.2582

|-
|}

The ''exo'' adduct is more stable than the ''endo'' adduct by 10.7 kJ mol-1. This is due to the presence of secondary overlap of frontier orbitals in the ''endo'' transition state, which is not present in the ''exo'' transition state.

Diagram ? - the interaction of frontier orbitals in the ''endo'' transition state

[[file:Endo_mechanism.png]]

The dashed lines in the diagram above denote bond-forming interactions, while the dotted lines donate non-bond forming secondary orbital interactions. In the endo transition state, only bond-forming interactions are present:

Diagram ? - the interaction of frontier orbitals in the ''exo'' transition state

[[File:Exo_mechanism.png]]

The HOMO of both ''endo'' and ''exo'' transition states have nodal planes. However, secondary overlap is hard to confirm from the calculated HOMO diagrams, as they all show a similar degree of overlap. This might be due to the choose of method and basis set which is not accurate enough to be able to illustrate the secondary interactions in the calculated diagram. Hence, another more accurate method should be used to examine the HOMOs of the two transition states.

Examine the shapes of the optimized ''endo'' and ''exo'' transition states, we can see that for the ''exo'' isomer, the maleic anhydride molecule fragment is on the same side as the CH2-CH2 group. This leads to large steric strain in the transition state. For the endo isomer, the maleic anhydride fragment is on the opposite side as the CH2-CH2 group, which avoids the steric strain.

Therefore, the relative energy of the transition states is depend on two factors: the extent of secondary interactions between the frontier orbitals, and the extent of steric strain. The fact that the ''exo'' adduct is more stable shows that the stabilizing effect by the secondary interactions is greater than the destabilizing effect by the steric hindrance.

=Reference=

Rep:Mod3:YJY1234

2011-11-11T16:12:04Z

Jy1109: /* Activation energies */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-calculate again! || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by (?).

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

Graph 3 -need to get the Newman projection view of the molecule in graph 2!

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || ??||-234.61170280

|-

|Energy/ kJ mol-1 ||??||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles. COMPARE THE ENERGIES AND RATIONALISE!

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

The boat transition structure is optimized using the QST2 method, which specifies the reactants and products for a reaction in attempt to calculate the transition state.
The DFT-B3LYP/6-31G(d) optmized ''anti2'' 1,5-hexadiene structure was duplicated, labelled and oriented so that they mimic the reactant and product. Then, the first QST2 calculation was run, but this job failed as the starting structures differed too much from the transition state. Therefore, the structure of the starting structures were modified so that they are closer to the boat transition state structure.

'''''Graph 7'' - the modified starting structures'''

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

The QST2 calculation was started again. This time, the transition state structure was successfully located.

'''''Graph 8'' - the boat transition state structure located using the QST2 method'''

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

===The IRC calculation===

Looking at this transition structure, as well as the structure for the chair transition state, it is impossible to predict which conformer will form. However, another method called the Intrinsic Coordinate (IRC) Method allows us to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

To find out the minimum energy path of the reaction, the IRC calculation was run for the chair transition state structure. However, after the calculation, the minimum geometry was not reached yet. The energy of the final structure is -231.68049221 a.u..

To continue minimizing in attempt to reach the minimum geometry, the last point on the IRC was taken to run a minimum minimization using the HF/3-21G level of theory.

Graph 9 - the final structure of the geometry optimization

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

The energy of this structure is -231.69166702 a.u., which is slightly lower than the starting structure. However, this is still not the minimum geometry.

Another attempt to obtain the minimimum geometry was to redo the IRC, specifying that force constants should be calculated at every step. After redoing the IRC, the geometry minimum was obtained.

Graph 10 - the final structure after redoing the IRC

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

The energy of this structure is -231.79116428 a.u.. The RMS gradient norm for the calculation is 0.00001145 a.u., which is less than 0.001 a.u., showing that the optimization is converged.
The first approach was much faster than the second approach, but as the starting structure was not close to the minimum structure to begin with, it was not able to locate the minimum structure. The second approach was more time-consuming, but it successfully calculated the minimum structure.

===Activation energies===

In this section, the activation energies for the reaction via both transition structures were calculated. Firstly, the chair and boat transition structure were reoptimized using the B3LYP/6-31G* level of theory and frequency calculations were carried out.The structures and energies of the optimized structures are compared with the geometry optimized using HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ Table 4 - comparing the chair transition structure optimized at two different levels of theory
! Level of theory !! Structure !! Energy/a.u. !! Energy/ kJ mol-1
|-
| HF/3-21G || [[File:Optimized_strcuture_for_b.PNG|300px]] || -231.680492 ||-608277.132
|-
| B3LYP/6-31G* ||[[File:Structure_after_optmiization_in_part_g.PNG|300px]]||-234.563120||-615845.472
|-
|}

The two structures are similar, but the energy optimized using B3LYP/6-31G* level of theory is 7730 kJ mol-1 lower.

{| class="wikitable" border="1"
|+ Table 5 - comparing the boat transition structure optimized at two different levels of theory
! Level of theory !! Structure !! Energy/a.u. !! Energy/ kJ mol-1
|-
| HF/3-21G || [[File:Trans_state_opt_after_modifying_angle.PNG|300px]] || -231.670907 ||-608251.966
|-
| B3LYP/6-31G* ||[[File:Boat_optimisation_g.png|300px]]||-234.6634537||-616108.898
|-
|}

The two structures are similar, but the energy optimized using B3LYP/6-31G* level of theory is 7857 kJ mol-1 lower.

The imaginary frequency of the reoptimized boat transition structure is -532 cm -1, while the imaginary frequency of the reoptimized chair structure is -567 cm-1.

{| class="wikitable" border="1"
|+ Table 6 - Summary of energies for the Ci (''anti 2'') reactant, chair and boat transition state
|-
!colspan="1"|
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
|
| '''Electronic energy/a.u.'''
| '''Sum of electronic and zero-point energies at 0K/a.u.'''
| '''Sum of electronic and thermal energies at 298.15K/a.u. '''
| '''Electronic energy/a.u.'''
| '''Sum of electronic and zero-point energies at 0K/a.u.'''
|'''Sum of electronic and thermal energies at 298.15K/a.u.'''
|-
| '''Chair Transition State'''
| align="center" |-231.680492
| align="center" |-231.527869
| align="center" |-231.522510
| align="center" |-234.563120
| align="center" |-234.421066
| align="center" |-234.415145
|-
| '''Boat Transition State'''
| align="center" |-231.670907
| align="center" |-231.519026
| align="center" |-231.510941
| align="center" |-234.663454
| align="center" |-234.522703
| align="center" |-234.516360
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.592535

| align="center" |-231.599506
| align="center" |-231.752501
| align="center" | -234.611702
| align="center" | -234.49195
| align="center" | -234.461849
|}

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_unfreeze_barny_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

d===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_endo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Endo_DFT_optimised_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05238788 || -0.0515048 || -612.68339675
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00272262 || 0.00000811 || 0.00000704
|-align="center"
| '''Dipole moment/ Debye''' || 6.0005 || 6.1660 || 6.1142
|-align="center"
|'''Job CPU time''' || 16 seconds || 3 seconds || 35 minutes 32 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.16 || 2.27
|-align="center"
|'''Imaginary frequency/ cm-1 '''|| - ||-806 || -447
|-
|}

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''endo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''endo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C5, C3 and C7 || 1.39 ||
|-
|C1 and C3 || 1.40||
|-
|C5 and C16, C13 and C7 || 1.52||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C13 and C16 || 1.56||
|-
|C11 and C20, C9 and C19 ||1.48 ||
|-
|C20 and O21, C19 and O21 || 1.40||
|-
|C19 and O22, C20 and O13 || 0.22 ||
|-

|}

'''Literature value!'''

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
'''

The HOMO and LUMO of the optimized ''endo'' transition state was calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Endo_HOMO.PNG|300px]] ||[[File:Endo_LUMO.PNG|300px]]
|-
| '''Symmetry''' || Antisymmetric || Antisymmetric
|-
|}

===Secondary orbital overlap effect===

Experimental observation is that the reaction between maleic anhydride and cyclopentadiene gives the ''endo'' adduct faster than they give the ''exo'' adduct even though the latter is more thermodynamically stable.(pp.106). This is because the transition state of the ''endo'' isomer is lower in energy, as show in the table below:
{| class="wikitable" border="1"
|+Table ? - The energies of the optimized transition states from the DFT-B3LYP/6-31G(d) optimization
! !! ''Exo'' adduct !! ''Endo'' adduct
|-
| Energy/a.u. ||-612.67931095|| -612.68339675

|-

| Energy/kJ mol-1 || -1608589.5309||-1608600.2582

|-
|}

The ''exo'' adduct is more stable than the ''endo'' adduct by 10.7 kJ mol-1. This is due to the presence of secondary overlap of frontier orbitals in the ''endo'' transition state, which is not present in the ''exo'' transition state.

Diagram ? - the interaction of frontier orbitals in the ''endo'' transition state

[[file:Endo_mechanism.png]]

The dashed lines in the diagram above denote bond-forming interactions, while the dotted lines donate non-bond forming secondary orbital interactions. In the endo transition state, only bond-forming interactions are present:

Diagram ? - the interaction of frontier orbitals in the ''exo'' transition state

[[File:Exo_mechanism.png]]

The HOMO of both ''endo'' and ''exo'' transition states have nodal planes. However, secondary overlap is hard to confirm from the calculated HOMO diagrams, as they all show a similar degree of overlap. This might be due to the choose of method and basis set which is not accurate enough to be able to illustrate the secondary interactions in the calculated diagram. Hence, another more accurate method should be used to examine the HOMOs of the two transition states.

Examine the shapes of the optimized ''endo'' and ''exo'' transition states, we can see that for the ''exo'' isomer, the maleic anhydride molecule fragment is on the same side as the CH2-CH2 group. This leads to large steric strain in the transition state. For the endo isomer, the maleic anhydride fragment is on the opposite side as the CH2-CH2 group, which avoids the steric strain.

Therefore, the relative energy of the transition states is depend on two factors: the extent of secondary interactions between the frontier orbitals, and the extent of steric strain. The fact that the ''exo'' adduct is more stable shows that the stabilizing effect by the secondary interactions is greater than the destabilizing effect by the steric hindrance.

=Reference=

File:Boat optimisation g.png

2011-11-11T14:40:55Z

Jy1109:

File:Structure after optmiization in part g.PNG

2011-11-11T14:30:15Z

Jy1109:

Rep:Mod3:YJY1234

2011-11-11T14:17:45Z

Jy1109: /* Optimizing the boat transition structure */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-calculate again! || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by (?).

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

Graph 3 -need to get the Newman projection view of the molecule in graph 2!

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || ??||-234.61170280

|-

|Energy/ kJ mol-1 ||??||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles. COMPARE THE ENERGIES AND RATIONALISE!

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

The boat transition structure is optimized using the QST2 method, which specifies the reactants and products for a reaction in attempt to calculate the transition state.
The DFT-B3LYP/6-31G(d) optmized ''anti2'' 1,5-hexadiene structure was duplicated, labelled and oriented so that they mimic the reactant and product. Then, the first QST2 calculation was run, but this job failed as the starting structures differed too much from the transition state. Therefore, the structure of the starting structures were modified so that they are closer to the boat transition state structure.

'''''Graph 7'' - the modified starting structures'''

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

The QST2 calculation was started again. This time, the transition state structure was successfully located.

'''''Graph 8'' - the boat transition state structure located using the QST2 method'''

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

===The IRC calculation===

Looking at this transition structure, as well as the structure for the chair transition state, it is impossible to predict which conformer will form. However, another method called the Intrinsic Coordinate (IRC) Method allows us to follow the minimum energy path from a transition structure down to its local minimum on a potential energy surface.

To find out the minimum energy path of the reaction, the IRC calculation was run for the chair transition state structure. However, after the calculation, the minimum geometry was not reached yet. The energy of the final structure is -231.68049221 a.u..

To continue minimizing in attempt to reach the minimum geometry, the last point on the IRC was taken to run a minimum minimization using the HF/3-21G level of theory.

Graph 9 - the final structure of the geometry optimization

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

The energy of this structure is -231.69166702 a.u., which is slightly lower than the starting structure. However, this is still not the minimum geometry.

Another attempt to obtain the minimimum geometry was to redo the IRC, specifying that force constants should be calculated at every step. After redoing the IRC, the geometry minimum was obtained.

Graph 10 - the final structure after redoing the IRC

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

The energy of this structure is -231.79116428 a.u.. The RMS gradient norm for the calculation is 0.00001145 a.u., which is less than 0.001 a.u., showing that the optimization is converged.
The first approach was much faster than the second approach, but as the starting structure was not close to the minimum structure to begin with, it was not able to locate the minimum structure. The second approach was more time-consuming, but it successfully calculated the minimum structure.

===Activation energies===

(g)
B3LYP/6-31G* of chair reoptimization =-234.61068420
Final structure captured

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_unfreeze_barny_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

d===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_endo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Endo_DFT_optimised_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05238788 || -0.0515048 || -612.68339675
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00272262 || 0.00000811 || 0.00000704
|-align="center"
| '''Dipole moment/ Debye''' || 6.0005 || 6.1660 || 6.1142
|-align="center"
|'''Job CPU time''' || 16 seconds || 3 seconds || 35 minutes 32 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.16 || 2.27
|-align="center"
|'''Imaginary frequency/ cm-1 '''|| - ||-806 || -447
|-
|}

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''endo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''endo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C5, C3 and C7 || 1.39 ||
|-
|C1 and C3 || 1.40||
|-
|C5 and C16, C13 and C7 || 1.52||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C13 and C16 || 1.56||
|-
|C11 and C20, C9 and C19 ||1.48 ||
|-
|C20 and O21, C19 and O21 || 1.40||
|-
|C19 and O22, C20 and O13 || 0.22 ||
|-

|}

'''Literature value!'''

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
'''

The HOMO and LUMO of the optimized ''endo'' transition state was calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Endo_HOMO.PNG|300px]] ||[[File:Endo_LUMO.PNG|300px]]
|-
| '''Symmetry''' || Antisymmetric || Antisymmetric
|-
|}

===Secondary orbital overlap effect===

Experimental observation is that the reaction between maleic anhydride and cyclopentadiene gives the ''endo'' adduct faster than they give the ''exo'' adduct even though the latter is more thermodynamically stable.(pp.106). This is because the transition state of the ''endo'' isomer is lower in energy, as show in the table below:
{| class="wikitable" border="1"
|+Table ? - The energies of the optimized transition states from the DFT-B3LYP/6-31G(d) optimization
! !! ''Exo'' adduct !! ''Endo'' adduct
|-
| Energy/a.u. ||-612.67931095|| -612.68339675

|-

| Energy/kJ mol-1 || -1608589.5309||-1608600.2582

|-
|}

The ''exo'' adduct is more stable than the ''endo'' adduct by 10.7 kJ mol-1. This is due to the presence of secondary overlap of frontier orbitals in the ''endo'' transition state, which is not present in the ''exo'' transition state.

Diagram ? - the interaction of frontier orbitals in the ''endo'' transition state

[[file:Endo_mechanism.png]]

The dashed lines in the diagram above denote bond-forming interactions, while the dotted lines donate non-bond forming secondary orbital interactions. In the endo transition state, only bond-forming interactions are present:

Diagram ? - the interaction of frontier orbitals in the ''exo'' transition state

[[File:Exo_mechanism.png]]

The HOMO of both ''endo'' and ''exo'' transition states have nodal planes. However, secondary overlap is hard to confirm from the calculated HOMO diagrams, as they all show a similar degree of overlap. This might be due to the choose of method and basis set which is not accurate enough to be able to illustrate the secondary interactions in the calculated diagram. Hence, another more accurate method should be used to examine the HOMOs of the two transition states.

Examine the shapes of the optimized ''endo'' and ''exo'' transition states, we can see that for the ''exo'' isomer, the maleic anhydride molecule fragment is on the same side as the CH2-CH2 group. This leads to large steric strain in the transition state. For the endo isomer, the maleic anhydride fragment is on the opposite side as the CH2-CH2 group, which avoids the steric strain.

Therefore, the relative energy of the transition states is depend on two factors: the extent of secondary interactions between the frontier orbitals, and the extent of steric strain. The fact that the ''exo'' adduct is more stable shows that the stabilizing effect by the secondary interactions is greater than the destabilizing effect by the steric hindrance.

=Reference=

File:IRC III.PNG

2011-11-11T14:14:15Z

Jy1109:

File:IRC i final structure.PNG

2011-11-11T12:47:36Z

Jy1109:

File:Trans state opt after modifying angle.PNG

2011-11-11T11:41:19Z

Jy1109:

File:Reactants and products after adjusting angles.PNG

2011-11-11T11:38:08Z

Jy1109:

File:Labelling the reactants and products.PNG

2011-11-11T11:28:57Z

Jy1109:

Rep:Mod3:YJY1234

2011-11-11T11:21:31Z

Jy1109: /* Secondary orbital overlap effect */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-calculate again! || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by (?).

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

Graph 3 -need to get the Newman projection view of the molecule in graph 2!

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || ??||-234.61170280

|-

|Energy/ kJ mol-1 ||??||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles. COMPARE THE ENERGIES AND RATIONALISE!

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

transitions state structure after modification of angles and optimization captured

After 1st IRC exercise, the structures are captured; graph showing that the optimization hasn't reach a minimum is captured. Energy after IRC exercise=-231.68049221 a.u.

"This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in."

Option (i)take the last point on the IRC and run a normal minimization
Final energy = -231.69166702 a.u.
structure captured

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum;

(iii) you can redo the IRC specifying that you want to compute the force constants at every step.

Calculating activation energy for the chair conformation
energy = -231.69166428 a.u.
RMS gradient norm = 0.00001145 - converged?

final structure captured

(g)
B3LYP/6-31G* of chair reoptimization =-234.61068420
Final structure captured

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_unfreeze_barny_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

d===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_endo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Endo_DFT_optimised_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05238788 || -0.0515048 || -612.68339675
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00272262 || 0.00000811 || 0.00000704
|-align="center"
| '''Dipole moment/ Debye''' || 6.0005 || 6.1660 || 6.1142
|-align="center"
|'''Job CPU time''' || 16 seconds || 3 seconds || 35 minutes 32 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.16 || 2.27
|-align="center"
|'''Imaginary frequency/ cm-1 '''|| - ||-806 || -447
|-
|}

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''endo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''endo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C5, C3 and C7 || 1.39 ||
|-
|C1 and C3 || 1.40||
|-
|C5 and C16, C13 and C7 || 1.52||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C13 and C16 || 1.56||
|-
|C11 and C20, C9 and C19 ||1.48 ||
|-
|C20 and O21, C19 and O21 || 1.40||
|-
|C19 and O22, C20 and O13 || 0.22 ||
|-

|}

'''Literature value!'''

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
'''

The HOMO and LUMO of the optimized ''endo'' transition state was calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Endo_HOMO.PNG|300px]] ||[[File:Endo_LUMO.PNG|300px]]
|-
| '''Symmetry''' || Antisymmetric || Antisymmetric
|-
|}

===Secondary orbital overlap effect===

Experimental observation is that the reaction between maleic anhydride and cyclopentadiene gives the ''endo'' adduct faster than they give the ''exo'' adduct even though the latter is more thermodynamically stable.(pp.106). This is because the transition state of the ''endo'' isomer is lower in energy, as show in the table below:
{| class="wikitable" border="1"
|+Table ? - The energies of the optimized transition states from the DFT-B3LYP/6-31G(d) optimization
! !! ''Exo'' adduct !! ''Endo'' adduct
|-
| Energy/a.u. ||-612.67931095|| -612.68339675

|-

| Energy/kJ mol-1 || -1608589.5309||-1608600.2582

|-
|}

The ''exo'' adduct is more stable than the ''endo'' adduct by 10.7 kJ mol-1. This is due to the presence of secondary overlap of frontier orbitals in the ''endo'' transition state, which is not present in the ''exo'' transition state.

Diagram ? - the interaction of frontier orbitals in the ''endo'' transition state

[[file:Endo_mechanism.png]]

The dashed lines in the diagram above denote bond-forming interactions, while the dotted lines donate non-bond forming secondary orbital interactions. In the endo transition state, only bond-forming interactions are present:

Diagram ? - the interaction of frontier orbitals in the ''exo'' transition state

[[File:Exo_mechanism.png]]

The HOMO of both ''endo'' and ''exo'' transition states have nodal planes. However, secondary overlap is hard to confirm from the calculated HOMO diagrams, as they all show a similar degree of overlap. This might be due to the choose of method and basis set which is not accurate enough to be able to illustrate the secondary interactions in the calculated diagram. Hence, another more accurate method should be used to examine the HOMOs of the two transition states.

Examine the shapes of the optimized ''endo'' and ''exo'' transition states, we can see that for the ''exo'' isomer, the maleic anhydride molecule fragment is on the same side as the CH2-CH2 group. This leads to large steric strain in the transition state. For the endo isomer, the maleic anhydride fragment is on the opposite side as the CH2-CH2 group, which avoids the steric strain.

Therefore, the relative energy of the transition states is depend on two factors: the extent of secondary interactions between the frontier orbitals, and the extent of steric strain. The fact that the ''exo'' adduct is more stable shows that the stabilizing effect by the secondary interactions is greater than the destabilizing effect by the steric hindrance.

=Reference=

Rep:Mod3:YJY1234

2011-11-11T11:21:00Z

Jy1109: /* Optimizing the endo transition state */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-calculate again! || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by (?).

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

Graph 3 -need to get the Newman projection view of the molecule in graph 2!

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || ??||-234.61170280

|-

|Energy/ kJ mol-1 ||??||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles. COMPARE THE ENERGIES AND RATIONALISE!

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

transitions state structure after modification of angles and optimization captured

After 1st IRC exercise, the structures are captured; graph showing that the optimization hasn't reach a minimum is captured. Energy after IRC exercise=-231.68049221 a.u.

"This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in."

Option (i)take the last point on the IRC and run a normal minimization
Final energy = -231.69166702 a.u.
structure captured

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum;

(iii) you can redo the IRC specifying that you want to compute the force constants at every step.

Calculating activation energy for the chair conformation
energy = -231.69166428 a.u.
RMS gradient norm = 0.00001145 - converged?

final structure captured

(g)
B3LYP/6-31G* of chair reoptimization =-234.61068420
Final structure captured

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_unfreeze_barny_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

d===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_endo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Endo_DFT_optimised_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05238788 || -0.0515048 || -612.68339675
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00272262 || 0.00000811 || 0.00000704
|-align="center"
| '''Dipole moment/ Debye''' || 6.0005 || 6.1660 || 6.1142
|-align="center"
|'''Job CPU time''' || 16 seconds || 3 seconds || 35 minutes 32 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.16 || 2.27
|-align="center"
|'''Imaginary frequency/ cm-1 '''|| - ||-806 || -447
|-
|}

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''endo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''endo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C5, C3 and C7 || 1.39 ||
|-
|C1 and C3 || 1.40||
|-
|C5 and C16, C13 and C7 || 1.52||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C13 and C16 || 1.56||
|-
|C11 and C20, C9 and C19 ||1.48 ||
|-
|C20 and O21, C19 and O21 || 1.40||
|-
|C19 and O22, C20 and O13 || 0.22 ||
|-

|}

'''Literature value!'''

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
'''

The HOMO and LUMO of the optimized ''endo'' transition state was calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Endo_HOMO.PNG|300px]] ||[[File:Endo_LUMO.PNG|300px]]
|-
| '''Symmetry''' || Antisymmetric || Antisymmetric
|-
|}

===Secondary orbital overlap effect===

Experimental observation is that the reaction between maleic anhydride and cyclopentadiene gives the ''endo'' adduct faster than they give the ''exo'' adduct even though the latter is more thermodynamically stable.(pp.106). This is because the transition state of the ''endo'' isomer is lower in energy, as show in the table below:
{| class="wikitable" border="1"
|+Table ? - The energies of the optimized transition states from the DFT-B3LYP/6-31G(d) optimization
! !! ''Exo'' adduct !! ''Endo'' adduct
|-
| Energy/a.u. || cell||-612.67931095|| -612.68339675

|-

| Energy/kJ mol-1 || -1608589.5309||-1608600.2582

|-
|}

The ''exo'' adduct is more stable than the ''endo'' adduct by 10.7 kJ mol-1. This is due to the presence of secondary overlap of frontier orbitals in the ''endo'' transition state, which is not present in the ''exo'' transition state.

Diagram ? - the interaction of frontier orbitals in the ''endo'' transition state

[[file:Endo_mechanism.png]]

The dashed lines in the diagram above denote bond-forming interactions, while the dotted lines donate non-bond forming secondary orbital interactions. In the endo transition state, only bond-forming interactions are present:

Diagram ? - the interaction of frontier orbitals in the ''exo'' transition state

[[File:Exo_mechanism.png]]

The HOMO of both ''endo'' and ''exo'' transition states have nodal planes. However, secondary overlap is hard to confirm from the calculated HOMO diagrams, as they all show a similar degree of overlap. This might be due to the choose of method and basis set which is not accurate enough to be able to illustrate the secondary interactions in the calculated diagram. Hence, another more accurate method should be used to examine the HOMOs of the two transition states.

Examine the shapes of the optimized ''endo'' and ''exo'' transition states, we can see that for the ''exo'' isomer, the maleic anhydride molecule fragment is on the same side as the CH2-CH2 group. This leads to large steric strain in the transition state. For the endo isomer, the maleic anhydride fragment is on the opposite side as the CH2-CH2 group, which avoids the steric strain.

Therefore, the relative energy of the transition states is depend on two factors: the extent of secondary interactions between the frontier orbitals, and the extent of steric strain. The fact that the ''exo'' adduct is more stable shows that the stabilizing effect by the secondary interactions is greater than the destabilizing effect by the steric hindrance.
=Reference=

File:Endo mechanism.png

2011-11-11T10:14:35Z

Jy1109: uploaded a new version of "File:Endo mechanism.png"

File:Endo mechanism.png

2011-11-11T07:53:56Z

Jy1109: uploaded a new version of "File:Endo mechanism.png"

Rep:Mod3:YJY1234

2011-11-10T19:51:54Z

Jy1109: /* Optimizing the endo transition state */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-calculate again! || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by (?).

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

Graph 3 -need to get the Newman projection view of the molecule in graph 2!

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || ??||-234.61170280

|-

|Energy/ kJ mol-1 ||??||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles. COMPARE THE ENERGIES AND RATIONALISE!

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

transitions state structure after modification of angles and optimization captured

After 1st IRC exercise, the structures are captured; graph showing that the optimization hasn't reach a minimum is captured. Energy after IRC exercise=-231.68049221 a.u.

"This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in."

Option (i)take the last point on the IRC and run a normal minimization
Final energy = -231.69166702 a.u.
structure captured

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum;

(iii) you can redo the IRC specifying that you want to compute the force constants at every step.

Calculating activation energy for the chair conformation
energy = -231.69166428 a.u.
RMS gradient norm = 0.00001145 - converged?

final structure captured

(g)
B3LYP/6-31G* of chair reoptimization =-234.61068420
Final structure captured

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_unfreeze_barny_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_endo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Endo_DFT_optimised_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05238788 || -0.0515048 || -612.68339675
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00272262 || 0.00000811 || 0.00000704
|-align="center"
| '''Dipole moment/ Debye''' || 6.0005 || 6.1660 || 6.1142
|-align="center"
|'''Job CPU time''' || 16 seconds || 3 seconds || 35 minutes 32 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.16 || 2.27
|-align="center"
|'''Imaginary frequency/ cm-1 '''|| - ||-806 || -447
|-
|}

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''endo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''endo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C5, C3 and C7 || 1.39 ||
|-
|C1 and C3 || 1.40||
|-
|C5 and C16, C13 and C7 || 1.52||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C13 and C16 || 1.56||
|-
|C11 and C20, C9 and C19 ||1.48 ||
|-
|C20 and O21, C19 and O21 || 1.40||
|-
|C19 and O22, C20 and O13 || 0.22 ||
|-

|}

'''Literature value!'''

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
'''

The HOMO and LUMO of the optimized ''endo'' transition state was calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Endo_LUMO.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the endo transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

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

Rep:Mod3:YJY1234

2011-11-10T19:49:44Z

Jy1109: /* Optimizing the endo transition state */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-calculate again! || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by (?).

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

Graph 3 -need to get the Newman projection view of the molecule in graph 2!

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || ??||-234.61170280

|-

|Energy/ kJ mol-1 ||??||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles. COMPARE THE ENERGIES AND RATIONALISE!

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

transitions state structure after modification of angles and optimization captured

After 1st IRC exercise, the structures are captured; graph showing that the optimization hasn't reach a minimum is captured. Energy after IRC exercise=-231.68049221 a.u.

"This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in."

Option (i)take the last point on the IRC and run a normal minimization
Final energy = -231.69166702 a.u.
structure captured

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum;

(iii) you can redo the IRC specifying that you want to compute the force constants at every step.

Calculating activation energy for the chair conformation
energy = -231.69166428 a.u.
RMS gradient norm = 0.00001145 - converged?

final structure captured

(g)
B3LYP/6-31G* of chair reoptimization =-234.61068420
Final structure captured

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_unfreeze_barny_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_endo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Endo_DFT_optimised_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05238788 || -0.0515048 || -612.68339675
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00272262 || 0.00000811 || 0.00000704
|-align="center"
| '''Dipole moment/ Debye''' || 6.0005 || 6.1660 || 6.1142
|-align="center"
|'''Job CPU time''' || 16 seconds || 3 seconds || 35 minutes 32 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.16 || 2.27
|-align="center"
|'''Imaginary frequency/ cm-1 。'''| - ||-806 || -447
|-
|}

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''endo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''endo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C5, C3 and C7 || 1.39 ||
|-
|C1 and C3 || 1.40||
|-
|C5 and C16, C13 and C7 || 1.52||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C13 and C16 || 1.56||
|-
|C11 and C20, C9 and C19 ||1.48 ||
|-
|C20 and O21, C19 and O21 || 1.40||
|-
|C19 and O22, C20 and O13 || 0.22 ||
|-

|}

'''Literature value!'''

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
'''

The HOMO and LUMO of the optimized ''endo'' transition state was calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Endo_LUMO.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the endo transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

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

File:Endo LUMO.PNG

2011-11-10T19:44:51Z

Jy1109:

File:Endo HOMO.PNG

2011-11-10T19:37:10Z

Jy1109:

File:Endo labelled structure.PNG

2011-11-10T19:28:40Z

Jy1109: uploaded a new version of "File:Endo labelled structure.PNG"

File:Endo labelled structure.PNG

2011-11-10T19:27:50Z

Jy1109:

Rep:Mod3:YJY1234

2011-11-10T18:47:04Z

Jy1109: /* Optimizing the exo transition state */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-calculate again! || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by (?).

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

Graph 3 -need to get the Newman projection view of the molecule in graph 2!

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || ??||-234.61170280

|-

|Energy/ kJ mol-1 ||??||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles. COMPARE THE ENERGIES AND RATIONALISE!

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

transitions state structure after modification of angles and optimization captured

After 1st IRC exercise, the structures are captured; graph showing that the optimization hasn't reach a minimum is captured. Energy after IRC exercise=-231.68049221 a.u.

"This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in."

Option (i)take the last point on the IRC and run a normal minimization
Final energy = -231.69166702 a.u.
structure captured

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum;

(iii) you can redo the IRC specifying that you want to compute the force constants at every step.

Calculating activation energy for the chair conformation
energy = -231.69166428 a.u.
RMS gradient norm = 0.00001145 - converged?

final structure captured

(g)
B3LYP/6-31G* of chair reoptimization =-234.61068420
Final structure captured

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_unfreeze_barny_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_endo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Endo_DFT_optimised_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05238788 || -0.0515048 || -612.68339675
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00272262 || 0.00000811 || 0.00000704
|-align="center"
| '''Dipole moment/ Debye''' || 6.0005 || 6.1660 || 6.1142
|-align="center"
|'''Job CPU time''' || 16 seconds || 3 seconds || 35 minutes 32 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.16 || 2.27
|-align="center"
|'''Imaginary frequency/ cm-1 |'''| - ||-806 || -447
|-
|}

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

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

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

-

Part (iii)

2.

Geometry analysis

Labelled diagram captured

1,5 =1.39A = 3,7 = 9,11

1,3 = 1.40A

5,16=1.52A=13,7

13,16=1.56

11,20=1.48= 9,19

20,21=1.40=19,21

19,22=0.22A=20,13

MO analysis

HOMO and LUMO caputred

File:Part iii opt of exo unfreeze barny structure.PNG

2011-11-10T18:45:55Z

Jy1109: uploaded a new version of "File:Part iii opt of exo unfreeze barny structure.PNG"

Rep:Mod3:YJY1234

2011-11-10T18:43:08Z

Jy1109: /* Optimizing the endo transition state */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-calculate again! || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by (?).

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

Graph 3 -need to get the Newman projection view of the molecule in graph 2!

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || ??||-234.61170280

|-

|Energy/ kJ mol-1 ||??||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles. COMPARE THE ENERGIES AND RATIONALISE!

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

transitions state structure after modification of angles and optimization captured

After 1st IRC exercise, the structures are captured; graph showing that the optimization hasn't reach a minimum is captured. Energy after IRC exercise=-231.68049221 a.u.

"This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in."

Option (i)take the last point on the IRC and run a normal minimization
Final energy = -231.69166702 a.u.
structure captured

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum;

(iii) you can redo the IRC specifying that you want to compute the force constants at every step.

Calculating activation energy for the chair conformation
energy = -231.69166428 a.u.
RMS gradient norm = 0.00001145 - converged?

final structure captured

(g)
B3LYP/6-31G* of chair reoptimization =-234.61068420
Final structure captured

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_endo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Endo_DFT_optimised_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05238788 || -0.0515048 || -612.68339675
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00272262 || 0.00000811 || 0.00000704
|-align="center"
| '''Dipole moment/ Debye''' || 6.0005 || 6.1660 || 6.1142
|-align="center"
|'''Job CPU time''' || 16 seconds || 3 seconds || 35 minutes 32 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.16 || 2.27
|-align="center"
|'''Imaginary frequency/ cm-1 |'''| - ||-806 || -447
|-
|}

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

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

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

-

Part (iii)

2.

Geometry analysis

Labelled diagram captured

1,5 =1.39A = 3,7 = 9,11

1,3 = 1.40A

5,16=1.52A=13,7

13,16=1.56

11,20=1.48= 9,19

20,21=1.40=19,21

19,22=0.22A=20,13

MO analysis

HOMO and LUMO caputred

File:Endo DFT optimised structure.PNG

2011-11-10T18:42:07Z

Jy1109: uploaded a new version of "File:Endo DFT optimised structure.PNG"

File:Endo DFT optimised structure.PNG

2011-11-10T18:40:32Z

Jy1109: uploaded a new version of "File:Endo DFT optimised structure.PNG"

File:Part iii opt of exo unfreeze barny structure.PNG

2011-11-10T18:34:47Z

Jy1109:

File:Part iii opt of endo freeze structure.PNG

2011-11-10T18:33:09Z

Jy1109:

File:Endo DFT optimised structure.PNG

2011-11-10T18:32:08Z

Jy1109:

Rep:Mod3:YJY1234

2011-11-10T18:23:58Z

Jy1109: /* Optimizing the endo transition state */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-calculate again! || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by (?).

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

Graph 3 -need to get the Newman projection view of the molecule in graph 2!

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || ??||-234.61170280

|-

|Energy/ kJ mol-1 ||??||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles. COMPARE THE ENERGIES AND RATIONALISE!

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

transitions state structure after modification of angles and optimization captured

After 1st IRC exercise, the structures are captured; graph showing that the optimization hasn't reach a minimum is captured. Energy after IRC exercise=-231.68049221 a.u.

"This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in."

Option (i)take the last point on the IRC and run a normal minimization
Final energy = -231.69166702 a.u.
structure captured

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum;

(iii) you can redo the IRC specifying that you want to compute the force constants at every step.

Calculating activation energy for the chair conformation
energy = -231.69166428 a.u.
RMS gradient norm = 0.00001145 - converged?

final structure captured

(g)
B3LYP/6-31G* of chair reoptimization =-234.61068420
Final structure captured

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

===Optimizing the ''endo'' transition state===

Same as optimizing the ''exo'' transition state, the ''endo'' transition state is optimized in a similar 3-step process: first, freeze the distance between the reaction coordinates to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. This is followed by unfreezing the and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The imaginary frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' ||[[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

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

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

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

-

Part (iii)

2.

Then, opt+freq, TS(barny), unfreeze coordinate;Opt=NoEigen; force constant = calculate once

calculated strcutre and calculation summary captured

Structure bond distance =2.16

Imaginary frequency = -806.45

Finally, run again using DFT/B3LYP/6-31G (d); TS(barny)

structure and cal summary captured

structure bond distanece = 2.27

Imaginary frequency = -447.02

Geometry analysis

Labelled diagram captured

1,5 =1.39A = 3,7 = 9,11

1,3 = 1.40A

5,16=1.52A=13,7

13,16=1.56

11,20=1.48= 9,19

20,21=1.40=19,21

19,22=0.22A=20,13

MO analysis

HOMO and LUMO caputred

Rep:Mod3:YJY1234

2011-11-10T16:51:05Z

Jy1109: /* Optimizing the exo transition state */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-calculate again! || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by (?).

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

Graph 3 -need to get the Newman projection view of the molecule in graph 2!

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || ??||-234.61170280

|-

|Energy/ kJ mol-1 ||??||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles. COMPARE THE ENERGIES AND RATIONALISE!

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

transitions state structure after modification of angles and optimization captured

After 1st IRC exercise, the structures are captured; graph showing that the optimization hasn't reach a minimum is captured. Energy after IRC exercise=-231.68049221 a.u.

"This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in."

Option (i)take the last point on the IRC and run a normal minimization
Final energy = -231.69166702 a.u.
structure captured

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum;

(iii) you can redo the IRC specifying that you want to compute the force constants at every step.

Calculating activation energy for the chair conformation
energy = -231.69166428 a.u.
RMS gradient norm = 0.00001145 - converged?

final structure captured

(g)
B3LYP/6-31G* of chair reoptimization =-234.61068420
Final structure captured

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

The HOMO of the ''exo'' transition state is formed from the LUMO of cyclohexa-1,3-diene and HOMO of maleic anhydride. The LUMO of the transition state is formed from the HOMO of cyclohexa-1,3-diene and LUMO of maleic anhydride.

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

===Optimizing the ''endo'' transition state===

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

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

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

-

Part (iii)

2.

After running, geometry analysis

labelled diagram captured

After geometry analysis, MO analysis

homo and lumo captured

3.Optimization of the endo TS

Step as before

Firstly, opt to minimum, freeze coordinate,

Opt=NoEigen

distance freeze to 2.2 A

structuer and calculation summary captured

structure bond distance = 2.20

Then, opt+freq, TS(barny), unfreeze coordinate;Opt=NoEigen; force constant = calculate once

calculated strcutre and calculation summary captured

Structure bond distance =2.16

Imaginary frequency = -806.45

Finally, run again using DFT/B3LYP/6-31G (d); TS(barny)

structure and cal summary captured

structure bond distanece = 2.27

Imaginary frequency = -447.02

Geometry analysis

Labelled diagram captured

1,5 =1.39A = 3,7 = 9,11

1,3 = 1.40A

5,16=1.52A=13,7

13,16=1.56

11,20=1.48= 9,19

20,21=1.40=19,21

19,22=0.22A=20,13

MO analysis

HOMO and LUMO caputred

Rep:Mod3:YJY1234

2011-11-10T16:45:19Z

Jy1109: /* Optimizing the exo transition state */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-calculate again! || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by (?).

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

Graph 3 -need to get the Newman projection view of the molecule in graph 2!

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || ??||-234.61170280

|-

|Energy/ kJ mol-1 ||??||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles. COMPARE THE ENERGIES AND RATIONALISE!

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

transitions state structure after modification of angles and optimization captured

After 1st IRC exercise, the structures are captured; graph showing that the optimization hasn't reach a minimum is captured. Energy after IRC exercise=-231.68049221 a.u.

"This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in."

Option (i)take the last point on the IRC and run a normal minimization
Final energy = -231.69166702 a.u.
structure captured

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum;

(iii) you can redo the IRC specifying that you want to compute the force constants at every step.

Calculating activation energy for the chair conformation
energy = -231.69166428 a.u.
RMS gradient norm = 0.00001145 - converged?

final structure captured

(g)
B3LYP/6-31G* of chair reoptimization =-234.61068420
Final structure captured

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-align = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization

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

{| class="wikitable" border="1"
|+ Table ? - Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|-
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! !! HOMO !! LUMO
|-
| '''Structure''' || [[File:Exo_HOMO.PNG|300px]] ||[[File:Exo_LUMO_sketch.PNG|300px]]
|-
| '''Symmetry''' || Symmetric || Antisymmetric
|-
|}

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

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

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

-

Part (iii)

2.

After running, geometry analysis

labelled diagram captured

After geometry analysis, MO analysis

homo and lumo captured

3.Optimization of the endo TS

Step as before

Firstly, opt to minimum, freeze coordinate,

Opt=NoEigen

distance freeze to 2.2 A

structuer and calculation summary captured

structure bond distance = 2.20

Then, opt+freq, TS(barny), unfreeze coordinate;Opt=NoEigen; force constant = calculate once

calculated strcutre and calculation summary captured

Structure bond distance =2.16

Imaginary frequency = -806.45

Finally, run again using DFT/B3LYP/6-31G (d); TS(barny)

structure and cal summary captured

structure bond distanece = 2.27

Imaginary frequency = -447.02

Geometry analysis

Labelled diagram captured

1,5 =1.39A = 3,7 = 9,11

1,3 = 1.40A

5,16=1.52A=13,7

13,16=1.56

11,20=1.48= 9,19

20,21=1.40=19,21

19,22=0.22A=20,13

MO analysis

HOMO and LUMO caputred

Rep:Mod3:YJY1234

2011-11-10T16:39:57Z

Jy1109: /* Optimizing the exo transition state */

mod 3

=The Cope Rearrangement Tutorial=

==Optimizing the reactants and products==

The "anti" and "gauche" conformation of 1,5-hexadiene is optimized at the HF/3-21G level of theory.

{| class="wikitable" border="1"
|+ ''Table 1'' - the two conformers of 1,5-hexadiene optimized using HF/3-21G
! Conformers !! Structure !! Energy/ a.u. !! Energy / kJ mol-1 !! Symmetry group
|-
| ''anti'' || [[File:App_optimization.PNG|300px]]|| -231.69253528||-calculate again! || Ci
|-
| ''gauche'' ||[[File:Gauche_optimization.PNG|300px]]||-231.69153035 || -608306.1128 || C2
|-
|}

The ''gauche'' conformation is expected to have a higher energy then the ''anti'' structure, as the eclipsing large groups are close to each other and results in steric clash which raises the energy. The calculation shows that the ''gauche'' conformation is indeed higher in energy by (?).

'''''Graph 1'' - the structure of the gauche 1,5-hexadiene in Newman projection'''

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

We can see that the structure in graph 1 can be further optimized by adjusting the positions of the two H2C=C groups to lower their steric clash. A new gauche conformer is drawn and optimized using HF/3-21G.

'''''Graph 2'' - Predicted lowest energy gauche conformation of 1,5-hexadiene'''

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

Graph 3 -need to get the Newman projection view of the molecule in graph 2!

The energy after optimization for the structure in graph 2 is -231.69266120 a.u., which is -608309.082 kJ mol-1. This is more stable than the structure in graph 2 by 2.97 kJ mol-1. The point group of the new structure is C1.

Comparing the optimized structure with the structures in Appendix 1, the first optimized gauche structure (as shown in graph 2) corresponds to the gauche 2 structure. The second optimized gauche structure (as shown in graph 3 and 4) corresponds to the gauche 3 structure.

The Ci anti2 conformation of 1,5-hexadiene was optimized at HF/3-21G level of theory in the section above. It is now optimized again using DFT-B3LYP/6-31G(d) level of theory. The energies and geometries of the two structures are compared in table 2.

{| class="wikitable" border="1"
|+ ''Table 2'' - comparison of the geometries and energies of anti2 conformation of 1,5-hexadiene optimized at HF/3-21G and DFT-B3LYP/6-31G(d)
! Level of theory !! HF/3-21G !!DFT-B3LYP/6-31G(d)
|-
|Structure ||[[File:App_optimization_-_labelled,HF,3-21G.PNG|300px]]||[[File:App_optimization_-labelled,DFT.PNG|300px]]
|-
| C=C bond length/Å || 1.32 ||1.33
|-
| C-C bond length/Å || 1.51 (C2-C5 and C9-C10); 1.55 (C5-C9) ||1.50 (C2-C5 and C9-C10 ), 1.55 (C5-C9)

|-

|C-H bond length/Å ||1.07-1.09 ||1.09-1.10

|-

|C(2,5,9) and C(5,9,10) dihedral angle/°||111.3 ||112.7

|-

|C(1,2,5 and 9,10,13) dihedral angle/° ||124.8 ||125.3

|-

|Energy/ a.u. || ??||-234.61170280

|-

|Energy/ kJ mol-1 ||??||-615973.026

|}

Reoptimization of the anti2 conformation of 1,5-hexadiene at the DFT-B3LYP/6-31G(d) level of theory results in no major change in geometry. The bond lengths are very similar (however in general, the reoptimized structure has slightly longer bond lengths). The dihedral angles are all very similar as well, although in general, the reoptimized structure has slightly larger dihedral angles. COMPARE THE ENERGIES AND RATIONALISE!

'''Vibrational frequency analysis'''

Frequency analysis shows that the optimized structure has no imaginary vibrations, only real ones. This conforms that the optimum structure was a minimum.

'''''Graph 4'' - the IR spectrum of C''i''' 'anti2'' conformation of 1, 5-hexadiene'''

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

{| class="wikitable" border="1"
|+ The thermochemistry of C''i''' 'anti2'' conformation of 1, 5-hexadiene
! Sum of electronic and zero-point energies/a.u.
| -234.469212
|-
! Sum of electronic and thermal energies/a.u.
| -234.461856
|-
! Sum of electronic and thermal enthalpies/a.u.
| -234.460912
|-
!Sum of electronic and thermal Free Energies/a.u.
| -234.500821
|-
|}

==Optimizing the "chair" and "boat" transition structures==

===Optimizaing the chair transition structure===

Firstly, an allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. The optimized allyl fragment was pasted twice and oriented into a structure that mimics the chair transition structure .

'''''Graph 5'' - the orientation of two allyl fragments to mimic the chair transition structure'''

[[File:Mimic_transition_state.PNG]]

The transition state was then manually optimized using two methods. The first method is to use Hartree Fock and the default basis set 3-21G . The second method is the frozen coordinate method.

====Using Hartree Fock and basis set 3-21G====

'''''Graph 6'' - the structure of the transition structure optimized using Hartree Fock and basis set 3-21G'''

[[File:Optimized_strcuture_for_b.PNG]]

The distance between atom [1] and [2] is 2.20Å. Frequency calculation of the optimized structure gave an imaginary frequency of magnitude -817.97 cm-1, which confirms that the transition state was successfully optimized. The movie for the vibration is recorded and can be accessed [[Media:Imaginary_frequency_in_part_b.gif |here]].

====Using the frozen coordinate method====

The transition structure is optimized again using the frozen coordinate method. The distances between the two terminal carbons on both sides of the transition structure was 'frozen', and then optimized. After the first optimization, the four terminal carbons were 'unfrozen', and the structure was optimized again.

The final optimized structure is the same as the structure optimized using Hartree Fock and 3-21G in graph 6, with the distance between the terminal carbons of the two allyl fragments 2.02A. This suggests that both methods are equally accurate for the boat transition structure.

===Optimizing the boat transition structure===

transitions state structure after modification of angles and optimization captured

After 1st IRC exercise, the structures are captured; graph showing that the optimization hasn't reach a minimum is captured. Energy after IRC exercise=-231.68049221 a.u.

"This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in."

Option (i)take the last point on the IRC and run a normal minimization
Final energy = -231.69166702 a.u.
structure captured

(ii) you can restart the IRC and specify a larger number of points until it reaches a minimum;

(iii) you can redo the IRC specifying that you want to compute the force constants at every step.

Calculating activation energy for the chair conformation
energy = -231.69166428 a.u.
RMS gradient norm = 0.00001145 - converged?

final structure captured

(g)
B3LYP/6-31G* of chair reoptimization =-234.61068420
Final structure captured

=The Diels Alder cycloaddition=

==Optimization and MO analysis of ''cis'' butadiene==

The optimization of cis butadiene is carried out using GaussView 5.0.9. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - the optimization of cis butadiene
! File type
| .log
|-
! Calculation type
| FOPT
|-
! Calculation method
| RAM1
|-
! Basis Set
|ZDO
|-
!Charge
|0
|-
!Spin
|Singlet
|-
!E(RAM1)/a.u.
| 0.04879719
|-
! RMS Gradient Norm/a.u.
|0.00001745
|-
!Dipole moment/ Debye
|0.0414
|-
!Job CPU time
|6.0 s
|-
|}

We can see that the optimization is converged, as the final RMS gradient is less than 0.001.

From the output checkpoint file of the optimization, we can visualize the molecular orbitals of ''cis'' butadiene. The HOMO and LUMO of the molecule are captured.

{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of ''cis'' butadiene
! !! HOMO !! LUMO
|-
| '''''cis'' butadiene''' || [[File:Part_i_HOMO.PNG|300px]] || [[File:Part_i_LUMO.PNG|300px]]
|-

|'''Symmetry with respect to molecular plane'''|| Antisymmetric || Antisymmetric
|-

|}

==Computation of the transition state geometry for the prototype reaction and an examination of the nature of the reaction path==

===Optimization of the transition state===
In this section, the transition state geometry for the following reaction is studied. An initial guess of the transition state structure is drawn in GaussView and optimized in a three step process.

Graph ? - the prototype reaction

[[File:Prototype_reac.png]]

Graph ? - an initial guess of the transition state structure of the prototype reaction

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

The transition state structure proposed is first optimized using the freeze coordinate method. The distance between carbon atom 7 and 14, as well as 1 and 11, is fixed to 2.1Å using the redundant coord editor in GaussView. The AM1 semi-empirical molecular orbital method was used for the calculation.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using the freeze coordinate method
! File type
| .log
|-
! Calculation Type
| FOPT
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11123824
|-
! RMS Gradient Norm/ a.u.
| 0.00342233
|-
! Dipole Moment/ Debye
| 0.5749
|-
! Job CPU time
| 14 s
|-

|}

Graph ? - the structure of the transition state after the first optimization

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

The structure is then reoptimized, which allows the bond distances that was previously frozen to be optimized. The optimization is to TS (berny), and used AM1 semi-empirical molecular orbital as the method.

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure after defrozing the reaction coordinates
! File type
| .log
|-
! Calculation Type
| FTS
|-
! Calculation method
|RAM1
|-
!Basis Set
| ZDO
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RAM1)/a.u.
| 0.11165464
|-
! RMS Gradient Norm/ a.u.
| 0.00001482
|-
! Dipole Moment/ Debye
| 0.5608
|-
! Job CPU time
| 33 s
|-

|}
Comparing the calculation summary of the first and second optimization, we can see a significant decrease in RMS gradient norm. After the first optimization, the RMS gradient norm is larger than 0.001 a.u., indicating that the optimization is not yet converged. After the second optimization, the RMS gradient norm is well below 0.001 a.u..

Graph ? - the structure of the transition state after the second optimization

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

After the second optimization, the transition state is optimized again, this time using a more accurate DFT/B3LYP/6-31G (d) level of theory. The frequency is also calculated

{| class="wikitable" border="1"
|+ Table ? - optimization of the transition state structure using DFT/B3LYP/6-31G (d) level of theory
! File type
| .log
|-
! Calculation Type
| FREQ
|-
! Calculation method
|RB3LYP
|-
!Basis Set
| 6-31G(d)
|-
! Charge
| 0
|-
! Spin
| Singlet
|-
! E (RB3LYP)/a.u.
| -234.54389655
|-
! RMS Gradient Norm/ a.u.
| 0.00000806
|-
! Dipole Moment/ Debye
| 0.3940
|-
! Job CPU time
| 6 minutes 48 seconds
|-

|}

Graph ? - the labelled structure of the transition state after the third optimization

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

The structure of the final optimized structure is analyzed and summarized in the table below.
{| class="wikitable" border="1"
|+ Table ? - Final optimized transition state structure
! C7 and C14, C1 and C11 bond distance/Å

| 2.27
|-
! C2 and C5 bond distance/Å

| 1.41
|-

!C1 and C2, C5 and C7 bond distance/Å

|1.38
|-

! C11 and C14 bond distance/Å

|1.39

|-

!C1,C2,C5,C7 dihedral angle/°

|0.0

|-

!C1,C2,C5 and C2,C5,C7 angle/°

|122.0

|-

|}

The imaginary frequency after the third optimization is -525 cm-1. The imaginary frequency is expected from a transition state. Animation of the vibration at -525 cm-1 shows that it corresponds to synchronous bond formation. (need to- INSERT ANIMATION?)

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

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

===Molecular Orbitals of the Transition State Structure===
{| class="wikitable" border="1"
|+ Table ? - the HOMO and LUMO of the transition state structure
! '''Molecular orbitals'''!! HOMO !! LUMO
|-
| '''Transition state''' || [[File:PART_ii_HOMO.PNG|300px]] || [[File:Part_ii_LUMO.PNG|300px]]
|-align="center"

|'''Symmetry with respect to molecular plane'''|| Symmetric || Symmetric
|-

|}

Comparing the shapes of the LUMO and HOMO with the HOMO and LUMO of ''cis'' butadiene and ethylene in table ? above, it can be seen that the LUMO is formed from ethylene HOMO orbital and butadiene LUMO orbital. (NEED TO COMPUTE MO of ethylene!!!) The HOMO is formed from ethylene HOMO and butadiene LUMO. These orbitals are allowed to interact because they have the same symmetry.

==Studying the regioselectivity of the Diels Alder Reaction==
In this section, the Diels-Alder reaction between cyclohexa-1,3-diene and maleic anhydride is studied.

Graph ? - the Diels Alder reaction between Cyclohexa-1,3-diene and Maleic Anhydride

[[File:Part_iii_reaction.png| 500 px]]

Two products are formed in the reaction. It is well known that the kinetic product, which is the ''endo'' product, is predominantly formed. The reaction is supposed to be kinetically controlled, with the ''exo'' transition state higher in energy.

The transition state for both the ''endo'' and the ''exo'' product was located. Their structures were optimized, and energy compared. The final geometry of the structures was also measured. The molecular molecules, especially the HOMO and LUMO, for the transition states were calculated using GaussView 5.0.9.

===Optimizing the reactants===

The reactants for this reaction, cyclohexa-1,3-diene and maleic anhydride is optimized using the semi-empirical AM1 method. The HOMOs and LUMOs are sketched.

{| class="wikitable" border="1" align="center"
|+ Table ? -The HOMOs and LUMOs of cyclohexa-1,3-diene and maleic anhydride
! colspan="1" |
! colspan="2" | cyclohexa-1,3-diene
! colspan="2" | maleic anhydride
|-align="center"
|'''Molecular Orbitals'''
|HOMO
|LUMO
|HOMO
|LUMO
|-align="center"
|'''Sketches'''
|[[File:Part_iii_cyclohex_HOMO.PNG|200px]]
|[[File:Part_iii_cyclohex_LUMO.PNG|200px]]
|[[File:Part_iii_maleic_HOMO.PNG|200px]]
|[[File:Part_iii_maleic_LUMO.PNG|200px]]
|-align="center"
|'''Symmetry'''
|Antisymmetric
|Symmetric
|Symmetric
|Antisymmetric
|-align="center"
|'''Energy of the optimized molecule/a.u.'''

|colspan="2" | 0.02771129
|colspan="2" | -0.12182423
|-

|}
Sketching the MOs of the reactants allows us to analyze the MOs of the transition state later and to determine which orbitals will be interacting to form the product.

===Optimizing the ''exo'' transition state===

The ''exo'' transition state was sketched in GaussView and optimized in a three-step process: firstly the distance between the reaction coordinates were freeze to 2.2Å using the Redundant Coord Editior and optimized to minimum using semi-empirical AM1 calculation method. After the first optimization, the reaction coordinates were unfrozen and optimized again to TS (berny) using semi-empirical AM1 calculation method. After this, the structure was optimized the third time to TS(berny) using a more accurate DFT-B3LYP/6-31G(d) level of theory. The frequency was also calculated when carrying out the third optimization.

{| class="wikitable" border="1"
|+ Table ? - Summary of calculation after each optimization
! !! Freeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (semi-empirical AM1) !! Unfreeze coordinate (DFT-B3LYP/6-31G(d))
|-align="center"
| '''Structure''' || [[File:Part_iii_opt_of_exo_freeze_structure.PNG|250px]]||[[File:Part_iii_opt_of_endo_unfreeze_TS_barney_structure.PNG|250px]]||[[File:Part_iii_opt_of_exo_DFT_structure.PNG|250px]]
|-align="center"
| '''File type '''|| .log || .log || .log
|-align="center"
|'''Calculation type''' || FOPT || FREQ || FREQ
|-align="center"
|'''Calculation method''' || RAM 1 || RAM 1 || RB3LYP
|-align="center"
|'''Basis set''' || ZDO || ZDO || 6-31G(d)
|-align="center"
|'''Charge''' || 0 || 0 || 0
|-align="center"
|'''Spin''' || Singlet || Singlet || Singlet
|-align="center"
|'''Energy/ a.u.''' || -0.05433384 || -0.05041984 || -612.67931095
|-align="center"
|'''RMS Gradient Norm/ a.u.''' || 0.00683174 || 0.00000499 || 0.00001134
|-align="center"
| '''Dipole moment/ Debye''' || 5.9268 || 5.5640 || 5.5496
|-align="center"
|'''Job CPU time''' || 27 seconds || 3 seconds || 31 minutes 8 seconds
|-align="center"
|'''Distance between the reaction coordinates/Å''' || 2.20 || 2.17 || 2.20
|-algin = "center"
|'''Imaginary frequency'''/ cm-1 || - ||-812 || -448

|-
|}

File for the final optimization can be found at {{DOI|10042/to-10181}}

After the second optimization, the distance between the reaction coordinates is 2.17Å. After the third optimization, the distance between the reaction coordinates is 2.20Å. The RMS Gradient Norm for the last optimization is less than 0.001, which proves that the optimization is converged.

After the optimization, the geometry of the optimized structure is analyzed.

Diagram ? - the labelled diagram of the ''exo'' transition state after optimization
[[File:Exo_labelled_diagram_for_geometry_analysis.PNG|500px]]

{| class="wikitable" border="1"
|+ Geometry analysis of the optimized ''exo'' transition state
! Bonds !! Bond lengths/ Å !! Literature / Å
|C1 and C3, C6 and C5 || 1.39 ||
|-
|C5 and C13 || 1.39||
|-
|C3 and C6 || 1.40||
|-
| C1 and C8, C10 and C15 || 1.51||
|-
|C8 and C10 || 1.56||
|-
|C13 and C17, C5 and C18 ||1.50
|-
|C18 and O19, C17 and O19 || 1.40||
|-
|C18 and O21, C17 and O20 || 1.20||
|-

|}

'''Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite”-CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo).
'''

The HOMO and LUMO of the optimized ''exo'' transition state is calculated using GaussView.

{| class="wikitable" border="1"
|+ Table ? - The HOMO and LUMO of the optimized ''exo'' transition state
! heading !! HOMO !! LUMO
|-
| Structure || [[=File:Exo_HOMO.PNG|300px]] !![[File:Exo_LUMO_sketch.PNG|300px||
|-
| Symmetry || Symmetric || Antisymmetric
|}

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

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

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

-

Part (iii)

2.

After running, geometry analysis

labelled diagram captured

After geometry analysis, MO analysis

homo and lumo captured

3.Optimization of the endo TS

Step as before

Firstly, opt to minimum, freeze coordinate,

Opt=NoEigen

distance freeze to 2.2 A

structuer and calculation summary captured

structure bond distance = 2.20

Then, opt+freq, TS(barny), unfreeze coordinate;Opt=NoEigen; force constant = calculate once

calculated strcutre and calculation summary captured

Structure bond distance =2.16

Imaginary frequency = -806.45

Finally, run again using DFT/B3LYP/6-31G (d); TS(barny)

structure and cal summary captured

structure bond distanece = 2.27

Imaginary frequency = -447.02

Geometry analysis

Labelled diagram captured

1,5 =1.39A = 3,7 = 9,11

1,3 = 1.40A

5,16=1.52A=13,7

13,16=1.56

11,20=1.48= 9,19

20,21=1.40=19,21

19,22=0.22A=20,13

MO analysis

HOMO and LUMO caputred

File:Exo LUMO sketch.PNG

2011-11-10T16:08:31Z

Jy1109:

File:Exo HOMO.PNG

2011-11-10T16:04:18Z

Jy1109:

File:Exo labelled diagram for geometry analysis.PNG

2011-11-10T11:12:43Z

Jy1109: uploaded a new version of "File:Exo labelled diagram for geometry analysis.PNG"

File:Exo labelled diagram for geometry analysis.PNG

2011-11-10T11:12:07Z

Jy1109:

Rep:Mod3:YJY1234

2011-11-10T10:26:23Z

Jy1109: /* Optimizing the exo transition state */

File:Part iii opt of exo freeze structure.PNG

2011-11-10T10:13:39Z

Jy1109: uploaded a new version of "File:Part iii opt of exo freeze structure.PNG"

File:Part iii opt of exo freeze structure.PNG

2011-11-10T10:12:41Z

Jy1109: uploaded a new version of "File:Part iii opt of exo freeze structure.PNG"

File:Part iii opt of exo freeze structure.PNG

2011-11-10T10:11:49Z

Jy1109: uploaded a new version of "File:Part iii opt of exo freeze structure.PNG"

File:Part iii opt of exo DFT structure.PNG

2011-11-10T10:07:45Z

Jy1109:

File:Part iii opt of endo unfreeze TS barney structure.PNG

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Jy1109:

File:Part iii opt of exo freeze structure.PNG

2011-11-10T10:02:23Z

Jy1109:

Rep:Mod3:YJY1234

2011-11-10T09:39:45Z

Jy1109: /* Studying the regioselectivity of the Diels Alder Reaction */

File:Part iii maleic LUMO.PNG

2011-11-10T09:00:48Z

Jy1109:

File:Part iii maleic HOMO.PNG

2011-11-10T08:59:37Z

Jy1109:

File:Part iii cyclohex LUMO.PNG

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