ChemWiki - User contributions [en]

Rep:Mod:seaunicorn13

2012-12-07T21:58:35Z

Vm1110: /* Activation Energies */

==Part 1: Cope Rearrangement==

===Optimising the reactants and products===

The following conformers of 1,5-hexadiene were drawn and optimised in GaussView, the given names correspond to those given in [[mod:phys3#Appendix_1|appendix 1]].
{| class="wikitable" border="1"
! Conformer
! ''Gauche1'' !! ''Gauche3'' !! ''Anti1'' !!
''Anti2''
|-
! Structure
| [[FILE:vm1110_hexadiene_gauche_1.png| 200px]] ||[[FILE:vm1110_hexadiene_gauche_3.png| 200px]]||[[FILE:vm1110_hexadiene_anti_1.png| 200px]]||[[FILE:vm1110_hexadiene_anti_2.png| 200px]]
|-
! Point Group
| C1||C1||C2||Ci
|-
! Energy/Hartree
| -231.688 || -231.693 || -231.693 || -231.693
|-
! Relative energy/kJmol-1
| 13.0||0||0.2||0.3
|-
! File link
| [[FILE:vm1110_hexadiene_gauche_1.log]]||[[FILE:vm1110_hexadiene_gauche_3.log]]|| [[FILE:vm1110_hexadiene_anti_1.log]]||[[FILE:vm1110_hexadiene_anti_2.log]]
|-
! File Summary
| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.68771617 au 
'''RMS Gradient Norm''': 0.00000295 au 
'''Dipole Moment''': 0.4554 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69266122 au 
'''RMS Gradient Norm''': 0.00000478 au 
'''Dipole Moment''': 0.3405 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69260236 au 
'''RMS Gradient Norm''': 0.00000559 au 
'''Dipole Moment''': 0.2021 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69253516 au 
'''RMS Gradient Norm''': 0.00004316 au 
'''Dipole Moment''': 0.000 Debye 
'''Job cpu time''': 5.0 Seconds 
|}
The energies obtained correspond to those given in [[mod:phys3#appendix_1|appendix 1]].

===Anti2 optimisation===

The anti2 conformer was optimised to a higher level of theory.

'''Optimisation file''' 
[[File:Vm1110_anti2_opt_631.log]] 
[[File:Vm1110_anti2_opt_631.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RB3LYP 
'''Basis Set''': 6-31G(d) 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -234.61171020 au 
'''RMS Gradient Norm''': 0.00001448 au 
'''Dipole Moment''': 0 Debye 
'''Point Group''': Ci 
'''Job cpu time''': 45.0 Seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
Predicted change in Energy=-2.577712D-08
Optimization completed.
-- Stationary point found.
</pre>

==== Energy and structure comparison ====
{| class="wikitable" border="1"
! !! HF 3-21G !! DFT 6-31G*
|-
! Point group
| Ci || Ci
|-
! Energy/HF
| -231.693 || -234.612
|-
! Relative Energy/kJmol-1
| 7664.3 || 0
|}

The energy from the B3LYP/6-31G* calculation is much lower than that from the HF/3-21G, however the structure is the same and retains the same symmetry. This shows that both levels of theory give the correct optimised structure but the higher level of theory gives a lower energy which is closer to the actual energy of the molecule in its optimised state.

===Optimising the 'chair' and 'boat' transition structures===
====Chair TS====
'''Allyl fragment optimisation''' 
[[File:Vm1110_allyl_opt.png|300px]] 
[[File:Vm1110_allyl_opt.log]] 
[[File:Vm1110_allyl_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': UHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -115.82303985 au 
'''RMS Gradient Norm''': 0.00008192 au 
'''Dipole Moment''': 0.0294 Debye 
'''Point Group''': C2 
'''Job cpu time''': 5.0 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000388 0.001200 YES
Predicted change in Energy=-2.083720D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Chair TS opt+freq''' 
Two fragments were arranged such that the central C atoms on each fragment were point outwards, away from one another, forming the chair transition state. The transition state was found and optimised by using the opt+freq job type, the Hartree Frock method and the 3-21G basis set. 
[[File:Vm1110_chair_opt.gif|300px]] 
(Click the enlarge and see vibration) 
[[File:Vm1110_chair_opt.log]] 
[[File:Vm1110_chair_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.61932241 au 
'''RMS Gradient Norm''': 0.00008192 au 
'''Dipole Moment''': 0.0006 Debye 
'''Point Group''': C1 
'''Job cpu time''': 19.0 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001795 0.001800 YES
RMS Displacement 0.000458 0.001200 YES
Predicted change in Energy=-6.233796D-08
Optimization completed.
-- Stationary point found.
</pre>
The imaginary frequency shown in the above image for the transition state occurs at -818cm-1 and shows the bond formation in the transition state. 
====Boat TS====
The boat transition state was optimised by using the optimised ''anti2'' conformer of 1,5-hexadiene and performing an opt+freq calculation using QST2 method. The first attempt with the optimised conformer with no alternations failed so the dihedral angle of the central C-C bond was rotated by 180° so that the molecules more closely resembled the boat transition state and could be more easily optimised. 
'''Failed Boast TS optimisation''' 
[[File:Vm1110_boat_opt_failed.log]] 
[[File:Vm1110_boat_opt_failed.chk]] 
'''Successful Boast TS optimisation''' 
[[File:Vm1110_boat_opt.gif|300px]] 
(Click the enlarge and see vibration) 
[[File:Vm1110_boat_opt.log]] 
[[File:Vm1110_boat_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.60280239 au 
'''RMS Gradient Norm''': 0.00003250 au 
'''Dipole Moment''': 0.1584 Debye 
'''Point Group''': CS 
'''Job cpu time''': 29.0 
The imaginary frequency shown in the above image for the transition state occurs at -840cm-1 and shows the bond formation in the transition state. 

==== IRC ====
An IRC calculation was performed on the optimised chair transition structure to confirm that the transition state was a maximum energy.
'''IRC''' 
[[File:Vm1110_chair_irc..png|400px]] 
[[File:Vm1110_chair_irc.log]] 
(checkpoint file too large to upload to wiki) 
'''File Type''': .log 
'''Calculation Type''': IRC 
'''Calculation Method''': 
'''Basis Set''': 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.61932241 au 
'''RMS Gradient Norm''': 0.00001799 au 
'''Dipole Moment''': 0.0006 Debye 
'''Point Group''': C1 
'''Job cpu time''': 16 minutes 38.0 seconds 
The graph above shows that the transition state found does indeed occupy the highest energy, hence it is the transition state. The IRC was calculated only in the forward direction because for this molecule it is symmetric. 

==== Activation Energies ====

'''Summary of energies (in au)'''
{| class="wikitable" border="1"
!
! colspan="1" | HF 3-21G
! colspan="1" | B3LYP 6-31G*
|-
! !!Electronic energy!!Electronic energy
|-
!Chair TS
| -231.61932241 || -234.5575872
|-
!Boat TS
| -231.60280239 || -234.5436851
|-
!''Anti2''
| -231.69253516 ||-234.61171020
|}

'''Summary of activation energies (in kJmol-1)'''

{| class="wikitable" border="1"
! !! HF 32-1G at 0K !! B3LYP 6-31G* at 0K !! Expt
|-
! Chair
| 192.6 || 142.1 || 140.2 ±2
|-
! Boat
| 235.9 || 178.6 || 187.0 ±8
|}

As can be seen, the results from the higher level of theory are much closer to experimental values.

==Part 2: Diels Alder==

=== Cis butadiene optimisation===
[[File:Vm1110_butadiene_opt.png|300px]]
==== Optimisation file ====
[[File:Vm1110_butadiene_opt.log]] 
[[File:Vm1110_butadiene_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': 0.04879719 au 
'''RMS Gradient Norm''': 0.00001742 au 
'''Dipole Moment''': 0.0414 Debye 
'''Point Group''': C2V 
'''Job cpu time''': 2.0 seconds 
==== Item table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000442 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-8.983482D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Molecular Orbitals ====

{| class="wikitable" border="1"
! !! HOMO !! LUMO
|-
!Orbital
|[[File:Vm1110_butadiene_HOMO.png|200px]] || [[File:Vm1110_butadiene_LUMO.png|200px]]
|-
! Symmetry
| Asymmetric || Symmetric
|}

 
=== Prototype reaction transition state ===

The transition state was investigated for the following reaction: 
[[File:Mb_da3.jpg|300px]] 
The correct geometry was found by drawing and cleaning up the bicyclo structure and removing one of the added ethylene fragments. The transition state was optimised and characterised using the opt+freq job type. The method used was semi-empirical AM1, as for the optimisation above.
==== Optimisation/frequency file ====
[[File:vm1110_prototype_ts.gif|300px]] 
[[File:Vm1110_prototype_ts.log]] 
[[File:Vm1110_prototype_ts.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': 0.11165464 au 
'''RMS Gradient Norm''': 0.00000030 au 
'''Dipole Moment''': 0.5605 Debye 
'''Point Group''': C1 
'''Job cpu time''': 3.0 seconds 
==== Item table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000028 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-9.870468D-12
Optimization completed.
-- Stationary point found.
</pre>

'''HOMO''' 
[[File:vm1110_prototype_HOMO.png|300px]] 
Asymmetric. Formed from the HOMO of the cis butadiene (AS, as seen above)) and the LUMO of the -CH2-CH2- fragment.
 
'''LUMO''' 
[[File:vm1110_prototype_lumo.png|300px]] 
Symmetric. Formed from the LUMO of the cis butadiene (S, as seen above)) and the HOMO of the -CH2-CH2- fragment.
 

==== Discussion ====

The optimisation converged and the frequency file gave a single imaginary vibration at -956cm-1 corresponding to the bond formation. The frequency also gave thermochemical information about the transition state, shown below.
<pre>
Sum of electronic and zero-point Energies= 0.253276
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015
</pre>
 
=== Diels Alder reaction with maleic anhydride ===

Maleic anhydride reacts with cyclohexa-1,3-diene in a diels alder mechanism to give an endo and an exo product. The reaction is kinetically controlled. Below the energies of the transition states for both the endo and the exo forms are compared.
==== Endo transition state ====
[[File:vm1110_endo_ts.gif|300px]] 
'''Optimisation''' 
[[File:Vm1110_endo_ts.log]] 
(Checkpoint file too large to put in wiki) 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -0.05150480 au 
'''RMS Gradient Norm''': 0.00000027 au 
'''Dipole Moment''': 0.5605 Debye 
'''Point Group''': C1 
'''Job cpu time''': 5.0 seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-5.113571D-12
Optimization completed.
-- Stationary point found.
</pre>

==== Exo transition state ====
[[File:vm1110_exo_ts.gif|300px]] 
'''Optimisation''' 
[[File:Vm1110_exo_ts.log]] 
(Checkpoint file too large to put in wiki) 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''':-0.05041968 au 
'''RMS Gradient Norm''': 0.00004220 au 
'''Dipole Moment''': 5.5647 Debye 
'''Point Group''': C1 
'''Job cpu time''': 11.0 seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001782 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-1.720725D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Discussion ====

{| class="wikitable" border="1"
|+ Molecular Orbitals
!
! colspan="2" | Endo
! colspan="2" | Exo
|-
! MOs
| [[File:vm1110_endo_homo.gif|150px]] HOMO || [[File:vm1110_endo_lumo.gif|150px]] LUMO ||[[File:vm1110_exo_homo.gif|150px]] HOMO || [[File:vm1110_exo_lumo.gif|150px]] LUMO
|}
As can be seen in the above table, the central oxygen on the maleic anhydride contributes less to the overall bonding and antibonding of the LUMO and HOMO for the exo product than the endo product. This is due to oxygen being highly electronegative.

{| class="wikitable" border="1"
|+ C-C distances
!
! Endo
! Exo
|-
! partially formed σ C-C bond
| 2.162 || 2.170
|-
! C-C through space distances
| 2.892 || 2.945
|-
! C-C single bond in cyclohexa-1,3-diene
| 1.393 || 1.394
|-
! C-C single bond in maleic anhydride
| 1.489 || 1.488
|}
The carbon Van der Waal radius of carbon is 1.7, compared to this the C-C distance through space is much shorter than the sum of two carbon Van der Waal radii. This means that there are forces holding the carbons closer together. This is due to secondary orbital overlap effect. This is more pronounced for the endo transition state which explains why it is lower in energy. 

{| class="wikitable" border="1"
|+ Relative energies
! !! Endo !! Exo
|-
! Energy/HF
| -0.052 || -0.050
|-
! Relative Energy/kJmol-1
| 0 || 2.849
|}
These relative energies show that the endo form is lower in energy and therefore more stabilised.

==== Ending comments ====

All of these calculations neglected solvent effects on the transition states and reactions. Solvents significantly effect the stability of transition states and hence change which product is more likely in a reaction.

Rep:Mod:seaunicorn13

2012-12-07T21:52:09Z

Vm1110: /* Discussion */

==Part 1: Cope Rearrangement==

===Optimising the reactants and products===

The following conformers of 1,5-hexadiene were drawn and optimised in GaussView, the given names correspond to those given in [[mod:phys3#Appendix_1|appendix 1]].
{| class="wikitable" border="1"
! Conformer
! ''Gauche1'' !! ''Gauche3'' !! ''Anti1'' !!
''Anti2''
|-
! Structure
| [[FILE:vm1110_hexadiene_gauche_1.png| 200px]] ||[[FILE:vm1110_hexadiene_gauche_3.png| 200px]]||[[FILE:vm1110_hexadiene_anti_1.png| 200px]]||[[FILE:vm1110_hexadiene_anti_2.png| 200px]]
|-
! Point Group
| C1||C1||C2||Ci
|-
! Energy/Hartree
| -231.688 || -231.693 || -231.693 || -231.693
|-
! Relative energy/kJmol-1
| 13.0||0||0.2||0.3
|-
! File link
| [[FILE:vm1110_hexadiene_gauche_1.log]]||[[FILE:vm1110_hexadiene_gauche_3.log]]|| [[FILE:vm1110_hexadiene_anti_1.log]]||[[FILE:vm1110_hexadiene_anti_2.log]]
|-
! File Summary
| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.68771617 au 
'''RMS Gradient Norm''': 0.00000295 au 
'''Dipole Moment''': 0.4554 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69266122 au 
'''RMS Gradient Norm''': 0.00000478 au 
'''Dipole Moment''': 0.3405 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69260236 au 
'''RMS Gradient Norm''': 0.00000559 au 
'''Dipole Moment''': 0.2021 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69253516 au 
'''RMS Gradient Norm''': 0.00004316 au 
'''Dipole Moment''': 0.000 Debye 
'''Job cpu time''': 5.0 Seconds 
|}
The energies obtained correspond to those given in [[mod:phys3#appendix_1|appendix 1]].

===Anti2 optimisation===

The anti2 conformer was optimised to a higher level of theory.

'''Optimisation file''' 
[[File:Vm1110_anti2_opt_631.log]] 
[[File:Vm1110_anti2_opt_631.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RB3LYP 
'''Basis Set''': 6-31G(d) 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -234.61171020 au 
'''RMS Gradient Norm''': 0.00001448 au 
'''Dipole Moment''': 0 Debye 
'''Point Group''': Ci 
'''Job cpu time''': 45.0 Seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
Predicted change in Energy=-2.577712D-08
Optimization completed.
-- Stationary point found.
</pre>

==== Energy and structure comparison ====
{| class="wikitable" border="1"
! !! HF 3-21G !! DFT 6-31G*
|-
! Point group
| Ci || Ci
|-
! Energy/HF
| -231.693 || -234.612
|-
! Relative Energy/kJmol-1
| 7664.3 || 0
|}

The energy from the B3LYP/6-31G* calculation is much lower than that from the HF/3-21G, however the structure is the same and retains the same symmetry. This shows that both levels of theory give the correct optimised structure but the higher level of theory gives a lower energy which is closer to the actual energy of the molecule in its optimised state.

===Optimising the 'chair' and 'boat' transition structures===
====Chair TS====
'''Allyl fragment optimisation''' 
[[File:Vm1110_allyl_opt.png|300px]] 
[[File:Vm1110_allyl_opt.log]] 
[[File:Vm1110_allyl_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': UHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -115.82303985 au 
'''RMS Gradient Norm''': 0.00008192 au 
'''Dipole Moment''': 0.0294 Debye 
'''Point Group''': C2 
'''Job cpu time''': 5.0 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000388 0.001200 YES
Predicted change in Energy=-2.083720D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Chair TS opt+freq''' 
Two fragments were arranged such that the central C atoms on each fragment were point outwards, away from one another, forming the chair transition state. The transition state was found and optimised by using the opt+freq job type, the Hartree Frock method and the 3-21G basis set. 
[[File:Vm1110_chair_opt.gif|300px]] 
(Click the enlarge and see vibration) 
[[File:Vm1110_chair_opt.log]] 
[[File:Vm1110_chair_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.61932241 au 
'''RMS Gradient Norm''': 0.00008192 au 
'''Dipole Moment''': 0.0006 Debye 
'''Point Group''': C1 
'''Job cpu time''': 19.0 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001795 0.001800 YES
RMS Displacement 0.000458 0.001200 YES
Predicted change in Energy=-6.233796D-08
Optimization completed.
-- Stationary point found.
</pre>
The imaginary frequency shown in the above image for the transition state occurs at -818cm-1 and shows the bond formation in the transition state. 
====Boat TS====
The boat transition state was optimised by using the optimised ''anti2'' conformer of 1,5-hexadiene and performing an opt+freq calculation using QST2 method. The first attempt with the optimised conformer with no alternations failed so the dihedral angle of the central C-C bond was rotated by 180° so that the molecules more closely resembled the boat transition state and could be more easily optimised. 
'''Failed Boast TS optimisation''' 
[[File:Vm1110_boat_opt_failed.log]] 
[[File:Vm1110_boat_opt_failed.chk]] 
'''Successful Boast TS optimisation''' 
[[File:Vm1110_boat_opt.gif|300px]] 
(Click the enlarge and see vibration) 
[[File:Vm1110_boat_opt.log]] 
[[File:Vm1110_boat_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.60280239 au 
'''RMS Gradient Norm''': 0.00003250 au 
'''Dipole Moment''': 0.1584 Debye 
'''Point Group''': CS 
'''Job cpu time''': 29.0 
The imaginary frequency shown in the above image for the transition state occurs at -840cm-1 and shows the bond formation in the transition state. 

==== IRC ====
An IRC calculation was performed on the optimised chair transition structure to confirm that the transition state was a maximum energy.
'''IRC''' 
[[File:Vm1110_chair_irc..png|400px]] 
[[File:Vm1110_chair_irc.log]] 
(checkpoint file too large to upload to wiki) 
'''File Type''': .log 
'''Calculation Type''': IRC 
'''Calculation Method''': 
'''Basis Set''': 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.61932241 au 
'''RMS Gradient Norm''': 0.00001799 au 
'''Dipole Moment''': 0.0006 Debye 
'''Point Group''': C1 
'''Job cpu time''': 16 minutes 38.0 seconds 
The graph above shows that the transition state found does indeed occupy the highest energy, hence it is the transition state. The IRC was calculated only in the forward direction because for this molecule it is symmetric. 

==== Activation Energies ====

'''Summary of energies'''
{| class="wikitable" border="1"
!
! colspan="1" | HF 3-21G
! colspan="1" | B3LYP 6-31G*
|-
! !!Electronic energy!!Electronic energy
|-
!Chair TS
| -231.61932241 || cell
|-
!Boat TS
| -231.60280239 || cell
|-
!''Anti2''
| -231.69253516 ||-234.61171020
|}

'''Summary of activation energies'''

{| class="wikitable" border="1"
! !! HF 32-1G at 0K !! B3LYP 6-31G* at 0K !! Expt
|-
! Chair
| 192.6 || cell || 140.2 ±2
|-
! Boat
| 235.9 || cell || 187.0 ±8
|}

==Part 2: Diels Alder==

=== Cis butadiene optimisation===
[[File:Vm1110_butadiene_opt.png|300px]]
==== Optimisation file ====
[[File:Vm1110_butadiene_opt.log]] 
[[File:Vm1110_butadiene_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': 0.04879719 au 
'''RMS Gradient Norm''': 0.00001742 au 
'''Dipole Moment''': 0.0414 Debye 
'''Point Group''': C2V 
'''Job cpu time''': 2.0 seconds 
==== Item table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000442 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-8.983482D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Molecular Orbitals ====

{| class="wikitable" border="1"
! !! HOMO !! LUMO
|-
!Orbital
|[[File:Vm1110_butadiene_HOMO.png|200px]] || [[File:Vm1110_butadiene_LUMO.png|200px]]
|-
! Symmetry
| Asymmetric || Symmetric
|}

 
=== Prototype reaction transition state ===

The transition state was investigated for the following reaction: 
[[File:Mb_da3.jpg|300px]] 
The correct geometry was found by drawing and cleaning up the bicyclo structure and removing one of the added ethylene fragments. The transition state was optimised and characterised using the opt+freq job type. The method used was semi-empirical AM1, as for the optimisation above.
==== Optimisation/frequency file ====
[[File:vm1110_prototype_ts.gif|300px]] 
[[File:Vm1110_prototype_ts.log]] 
[[File:Vm1110_prototype_ts.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': 0.11165464 au 
'''RMS Gradient Norm''': 0.00000030 au 
'''Dipole Moment''': 0.5605 Debye 
'''Point Group''': C1 
'''Job cpu time''': 3.0 seconds 
==== Item table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000028 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-9.870468D-12
Optimization completed.
-- Stationary point found.
</pre>

'''HOMO''' 
[[File:vm1110_prototype_HOMO.png|300px]] 
Asymmetric. Formed from the HOMO of the cis butadiene (AS, as seen above)) and the LUMO of the -CH2-CH2- fragment.
 
'''LUMO''' 
[[File:vm1110_prototype_lumo.png|300px]] 
Symmetric. Formed from the LUMO of the cis butadiene (S, as seen above)) and the HOMO of the -CH2-CH2- fragment.
 

==== Discussion ====

The optimisation converged and the frequency file gave a single imaginary vibration at -956cm-1 corresponding to the bond formation. The frequency also gave thermochemical information about the transition state, shown below.
<pre>
Sum of electronic and zero-point Energies= 0.253276
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015
</pre>
 
=== Diels Alder reaction with maleic anhydride ===

Maleic anhydride reacts with cyclohexa-1,3-diene in a diels alder mechanism to give an endo and an exo product. The reaction is kinetically controlled. Below the energies of the transition states for both the endo and the exo forms are compared.
==== Endo transition state ====
[[File:vm1110_endo_ts.gif|300px]] 
'''Optimisation''' 
[[File:Vm1110_endo_ts.log]] 
(Checkpoint file too large to put in wiki) 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -0.05150480 au 
'''RMS Gradient Norm''': 0.00000027 au 
'''Dipole Moment''': 0.5605 Debye 
'''Point Group''': C1 
'''Job cpu time''': 5.0 seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-5.113571D-12
Optimization completed.
-- Stationary point found.
</pre>

==== Exo transition state ====
[[File:vm1110_exo_ts.gif|300px]] 
'''Optimisation''' 
[[File:Vm1110_exo_ts.log]] 
(Checkpoint file too large to put in wiki) 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''':-0.05041968 au 
'''RMS Gradient Norm''': 0.00004220 au 
'''Dipole Moment''': 5.5647 Debye 
'''Point Group''': C1 
'''Job cpu time''': 11.0 seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001782 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-1.720725D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Discussion ====

{| class="wikitable" border="1"
|+ Molecular Orbitals
!
! colspan="2" | Endo
! colspan="2" | Exo
|-
! MOs
| [[File:vm1110_endo_homo.gif|150px]] HOMO || [[File:vm1110_endo_lumo.gif|150px]] LUMO ||[[File:vm1110_exo_homo.gif|150px]] HOMO || [[File:vm1110_exo_lumo.gif|150px]] LUMO
|}
As can be seen in the above table, the central oxygen on the maleic anhydride contributes less to the overall bonding and antibonding of the LUMO and HOMO for the exo product than the endo product. This is due to oxygen being highly electronegative.

{| class="wikitable" border="1"
|+ C-C distances
!
! Endo
! Exo
|-
! partially formed σ C-C bond
| 2.162 || 2.170
|-
! C-C through space distances
| 2.892 || 2.945
|-
! C-C single bond in cyclohexa-1,3-diene
| 1.393 || 1.394
|-
! C-C single bond in maleic anhydride
| 1.489 || 1.488
|}
The carbon Van der Waal radius of carbon is 1.7, compared to this the C-C distance through space is much shorter than the sum of two carbon Van der Waal radii. This means that there are forces holding the carbons closer together. This is due to secondary orbital overlap effect. This is more pronounced for the endo transition state which explains why it is lower in energy. 

{| class="wikitable" border="1"
|+ Relative energies
! !! Endo !! Exo
|-
! Energy/HF
| -0.052 || -0.050
|-
! Relative Energy/kJmol-1
| 0 || 2.849
|}
These relative energies show that the endo form is lower in energy and therefore more stabilised.

==== Ending comments ====

All of these calculations neglected solvent effects on the transition states and reactions. Solvents significantly effect the stability of transition states and hence change which product is more likely in a reaction.

Rep:Mod:seaunicorn13

2012-12-07T21:48:48Z

Vm1110: /* Item table */

==Part 1: Cope Rearrangement==

===Optimising the reactants and products===

The following conformers of 1,5-hexadiene were drawn and optimised in GaussView, the given names correspond to those given in [[mod:phys3#Appendix_1|appendix 1]].
{| class="wikitable" border="1"
! Conformer
! ''Gauche1'' !! ''Gauche3'' !! ''Anti1'' !!
''Anti2''
|-
! Structure
| [[FILE:vm1110_hexadiene_gauche_1.png| 200px]] ||[[FILE:vm1110_hexadiene_gauche_3.png| 200px]]||[[FILE:vm1110_hexadiene_anti_1.png| 200px]]||[[FILE:vm1110_hexadiene_anti_2.png| 200px]]
|-
! Point Group
| C1||C1||C2||Ci
|-
! Energy/Hartree
| -231.688 || -231.693 || -231.693 || -231.693
|-
! Relative energy/kJmol-1
| 13.0||0||0.2||0.3
|-
! File link
| [[FILE:vm1110_hexadiene_gauche_1.log]]||[[FILE:vm1110_hexadiene_gauche_3.log]]|| [[FILE:vm1110_hexadiene_anti_1.log]]||[[FILE:vm1110_hexadiene_anti_2.log]]
|-
! File Summary
| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.68771617 au 
'''RMS Gradient Norm''': 0.00000295 au 
'''Dipole Moment''': 0.4554 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69266122 au 
'''RMS Gradient Norm''': 0.00000478 au 
'''Dipole Moment''': 0.3405 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69260236 au 
'''RMS Gradient Norm''': 0.00000559 au 
'''Dipole Moment''': 0.2021 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69253516 au 
'''RMS Gradient Norm''': 0.00004316 au 
'''Dipole Moment''': 0.000 Debye 
'''Job cpu time''': 5.0 Seconds 
|}
The energies obtained correspond to those given in [[mod:phys3#appendix_1|appendix 1]].

===Anti2 optimisation===

The anti2 conformer was optimised to a higher level of theory.

'''Optimisation file''' 
[[File:Vm1110_anti2_opt_631.log]] 
[[File:Vm1110_anti2_opt_631.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RB3LYP 
'''Basis Set''': 6-31G(d) 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -234.61171020 au 
'''RMS Gradient Norm''': 0.00001448 au 
'''Dipole Moment''': 0 Debye 
'''Point Group''': Ci 
'''Job cpu time''': 45.0 Seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
Predicted change in Energy=-2.577712D-08
Optimization completed.
-- Stationary point found.
</pre>

==== Energy and structure comparison ====
{| class="wikitable" border="1"
! !! HF 3-21G !! DFT 6-31G*
|-
! Point group
| Ci || Ci
|-
! Energy/HF
| -231.693 || -234.612
|-
! Relative Energy/kJmol-1
| 7664.3 || 0
|}

The energy from the B3LYP/6-31G* calculation is much lower than that from the HF/3-21G, however the structure is the same and retains the same symmetry. This shows that both levels of theory give the correct optimised structure but the higher level of theory gives a lower energy which is closer to the actual energy of the molecule in its optimised state.

===Optimising the 'chair' and 'boat' transition structures===
====Chair TS====
'''Allyl fragment optimisation''' 
[[File:Vm1110_allyl_opt.png|300px]] 
[[File:Vm1110_allyl_opt.log]] 
[[File:Vm1110_allyl_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': UHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -115.82303985 au 
'''RMS Gradient Norm''': 0.00008192 au 
'''Dipole Moment''': 0.0294 Debye 
'''Point Group''': C2 
'''Job cpu time''': 5.0 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000388 0.001200 YES
Predicted change in Energy=-2.083720D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Chair TS opt+freq''' 
Two fragments were arranged such that the central C atoms on each fragment were point outwards, away from one another, forming the chair transition state. The transition state was found and optimised by using the opt+freq job type, the Hartree Frock method and the 3-21G basis set. 
[[File:Vm1110_chair_opt.gif|300px]] 
(Click the enlarge and see vibration) 
[[File:Vm1110_chair_opt.log]] 
[[File:Vm1110_chair_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.61932241 au 
'''RMS Gradient Norm''': 0.00008192 au 
'''Dipole Moment''': 0.0006 Debye 
'''Point Group''': C1 
'''Job cpu time''': 19.0 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001795 0.001800 YES
RMS Displacement 0.000458 0.001200 YES
Predicted change in Energy=-6.233796D-08
Optimization completed.
-- Stationary point found.
</pre>
The imaginary frequency shown in the above image for the transition state occurs at -818cm-1 and shows the bond formation in the transition state. 
====Boat TS====
The boat transition state was optimised by using the optimised ''anti2'' conformer of 1,5-hexadiene and performing an opt+freq calculation using QST2 method. The first attempt with the optimised conformer with no alternations failed so the dihedral angle of the central C-C bond was rotated by 180° so that the molecules more closely resembled the boat transition state and could be more easily optimised. 
'''Failed Boast TS optimisation''' 
[[File:Vm1110_boat_opt_failed.log]] 
[[File:Vm1110_boat_opt_failed.chk]] 
'''Successful Boast TS optimisation''' 
[[File:Vm1110_boat_opt.gif|300px]] 
(Click the enlarge and see vibration) 
[[File:Vm1110_boat_opt.log]] 
[[File:Vm1110_boat_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.60280239 au 
'''RMS Gradient Norm''': 0.00003250 au 
'''Dipole Moment''': 0.1584 Debye 
'''Point Group''': CS 
'''Job cpu time''': 29.0 
The imaginary frequency shown in the above image for the transition state occurs at -840cm-1 and shows the bond formation in the transition state. 

==== IRC ====
An IRC calculation was performed on the optimised chair transition structure to confirm that the transition state was a maximum energy.
'''IRC''' 
[[File:Vm1110_chair_irc..png|400px]] 
[[File:Vm1110_chair_irc.log]] 
(checkpoint file too large to upload to wiki) 
'''File Type''': .log 
'''Calculation Type''': IRC 
'''Calculation Method''': 
'''Basis Set''': 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.61932241 au 
'''RMS Gradient Norm''': 0.00001799 au 
'''Dipole Moment''': 0.0006 Debye 
'''Point Group''': C1 
'''Job cpu time''': 16 minutes 38.0 seconds 
The graph above shows that the transition state found does indeed occupy the highest energy, hence it is the transition state. The IRC was calculated only in the forward direction because for this molecule it is symmetric. 

==== Activation Energies ====

'''Summary of energies'''
{| class="wikitable" border="1"
!
! colspan="1" | HF 3-21G
! colspan="1" | B3LYP 6-31G*
|-
! !!Electronic energy!!Electronic energy
|-
!Chair TS
| -231.61932241 || cell
|-
!Boat TS
| -231.60280239 || cell
|-
!''Anti2''
| -231.69253516 ||-234.61171020
|}

'''Summary of activation energies'''

{| class="wikitable" border="1"
! !! HF 32-1G at 0K !! B3LYP 6-31G* at 0K !! Expt
|-
! Chair
| 192.6 || cell || 140.2 ±2
|-
! Boat
| 235.9 || cell || 187.0 ±8
|}

==Part 2: Diels Alder==

=== Cis butadiene optimisation===
[[File:Vm1110_butadiene_opt.png|300px]]
==== Optimisation file ====
[[File:Vm1110_butadiene_opt.log]] 
[[File:Vm1110_butadiene_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': 0.04879719 au 
'''RMS Gradient Norm''': 0.00001742 au 
'''Dipole Moment''': 0.0414 Debye 
'''Point Group''': C2V 
'''Job cpu time''': 2.0 seconds 
==== Item table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000442 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-8.983482D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Molecular Orbitals ====

{| class="wikitable" border="1"
! !! HOMO !! LUMO
|-
!Orbital
|[[File:Vm1110_butadiene_HOMO.png|200px]] || [[File:Vm1110_butadiene_LUMO.png|200px]]
|-
! Symmetry
| Asymmetric || Symmetric
|}

 
=== Prototype reaction transition state ===

The transition state was investigated for the following reaction: 
[[File:Mb_da3.jpg|300px]] 
The correct geometry was found by drawing and cleaning up the bicyclo structure and removing one of the added ethylene fragments. The transition state was optimised and characterised using the opt+freq job type. The method used was semi-empirical AM1, as for the optimisation above.
==== Optimisation/frequency file ====
[[File:vm1110_prototype_ts.gif|300px]] 
[[File:Vm1110_prototype_ts.log]] 
[[File:Vm1110_prototype_ts.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': 0.11165464 au 
'''RMS Gradient Norm''': 0.00000030 au 
'''Dipole Moment''': 0.5605 Debye 
'''Point Group''': C1 
'''Job cpu time''': 3.0 seconds 
==== Item table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000028 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-9.870468D-12
Optimization completed.
-- Stationary point found.
</pre>

'''HOMO''' 
[[File:vm1110_prototype_HOMO.png|300px]] 
Asymmetric. Formed from the HOMO of the cis butadiene (AS, as seen above)) and the LUMO of the -CH2-CH2- fragment.
 
'''LUMO''' 
[[File:vm1110_prototype_lumo.png|300px]] 
Symmetric. Formed from the LUMO of the cis butadiene (S, as seen above)) and the HOMO of the -CH2-CH2- fragment.
 

==== Discussion ====

The optimisation converged and the frequency file gave a single imaginary vibration at -956cm-1 corresponding to the bond formation. The frequency also gave thermochemical information about the transition state, shown below.
<pre>
Sum of electronic and zero-point Energies= 0.253276
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015
</pre>
 
=== Diels Alder reaction with maleic anhydride ===

Maleic anhydride reacts with cyclohexa-1,3-diene in a diels alder mechanism to give an endo and an exo product. The reaction is kinetically controlled. Below the energies of the transition states for both the endo and the exo forms are compared.
==== Endo transition state ====
[[File:vm1110_endo_ts.gif|300px]] 
'''Optimisation''' 
[[File:Vm1110_endo_ts.log]] 
(Checkpoint file too large to put in wiki) 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -0.05150480 au 
'''RMS Gradient Norm''': 0.00000027 au 
'''Dipole Moment''': 0.5605 Debye 
'''Point Group''': C1 
'''Job cpu time''': 5.0 seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-5.113571D-12
Optimization completed.
-- Stationary point found.
</pre>

==== Exo transition state ====
[[File:vm1110_exo_ts.gif|300px]] 
'''Optimisation''' 
[[File:Vm1110_exo_ts.log]] 
(Checkpoint file too large to put in wiki) 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''':-0.05041968 au 
'''RMS Gradient Norm''': 0.00004220 au 
'''Dipole Moment''': 5.5647 Debye 
'''Point Group''': C1 
'''Job cpu time''': 11.0 seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001782 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-1.720725D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Discussion ====

{| class="wikitable" border="1"
|+ Molecular Orbitals
!
! colspan="2" | Endo
! colspan="2" | Exo
|-
! MOs
| [[File:vm1110_endo_homo.gif|150px]] HOMO || [[File:vm1110_endo_lumo.gif|150px]] LUMO ||[[File:vm1110_exo_homo.gif|150px]] HOMO || [[File:vm1110_exo_lumo.gif|150px]] LUMO
|}
As can be seen in the above table, the central oxygen on the maleic anhydride contributes less to the overall bonding and antibonding of the LUMO and HOMO for the exo product than the endo product. This is due to oxygen being highly electronegative.

{| class="wikitable" border="1"
|+ C-C distances
!
! Endo
! Exo
|-
! partially formed σ C-C bond
| 2.162 || 2.170
|-
! C-C through space distances
| 2.892 || 2.945
|-
! C-C single bond in cyclohexa-1,3-diene
| 1.393 || 1.394
|-
! C-C single bond in maleic anhydride
| 1.489 || 1.488
|}
The carbon Van der Waal radius of carbon is 1.7, compared to this the C-C distance through space is much shorter than the sum of two carbon Van der Waal radii. This means that there are forces holding the carbons closer together. This is due to secondary orbital overlap effect. This is more pronounced for the endo transition state which explains why it is lower in energy. 

{| class="wikitable" border="1"
|+ Relative energies
! !! Endo !! Exo
|-
! Energy/HF
| -0.052 || -0.050
|-
! Relative Energy/kJmol-1
| 0 || 2.849
|}
These relative energies show that the endo form is lower in energy and therefore more stabilised.

Rep:Mod:seaunicorn13

2012-12-07T20:13:07Z

Vm1110: /* Discussion */

==Part 1: Cope Rearrangement==

===Optimising the reactants and products===

The following conformers of 1,5-hexadiene were drawn and optimised in GaussView, the given names correspond to those given in [[mod:phys3#Appendix_1|appendix 1]].
{| class="wikitable" border="1"
! Conformer
! ''Gauche1'' !! ''Gauche3'' !! ''Anti1'' !!
''Anti2''
|-
! Structure
| [[FILE:vm1110_hexadiene_gauche_1.png| 200px]] ||[[FILE:vm1110_hexadiene_gauche_3.png| 200px]]||[[FILE:vm1110_hexadiene_anti_1.png| 200px]]||[[FILE:vm1110_hexadiene_anti_2.png| 200px]]
|-
! Point Group
| C1||C1||C2||Ci
|-
! Energy/Hartree
| -231.688 || -231.693 || -231.693 || -231.693
|-
! Relative energy/kJmol-1
| 13.0||0||0.2||0.3
|-
! File link
| [[FILE:vm1110_hexadiene_gauche_1.log]]||[[FILE:vm1110_hexadiene_gauche_3.log]]|| [[FILE:vm1110_hexadiene_anti_1.log]]||[[FILE:vm1110_hexadiene_anti_2.log]]
|-
! File Summary
| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.68771617 au 
'''RMS Gradient Norm''': 0.00000295 au 
'''Dipole Moment''': 0.4554 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69266122 au 
'''RMS Gradient Norm''': 0.00000478 au 
'''Dipole Moment''': 0.3405 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69260236 au 
'''RMS Gradient Norm''': 0.00000559 au 
'''Dipole Moment''': 0.2021 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69253516 au 
'''RMS Gradient Norm''': 0.00004316 au 
'''Dipole Moment''': 0.000 Debye 
'''Job cpu time''': 5.0 Seconds 
|}
The energies obtained correspond to those given in [[mod:phys3#appendix_1|appendix 1]].

===Anti2 optimisation===

The anti2 conformer was optimised to a higher level of theory.

'''Optimisation file''' 
[[File:Vm1110_anti2_opt_631.log]] 
[[File:Vm1110_anti2_opt_631.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RB3LYP 
'''Basis Set''': 6-31G(d) 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -234.61171020 au 
'''RMS Gradient Norm''': 0.00001448 au 
'''Dipole Moment''': 0 Debye 
'''Point Group''': Ci 
'''Job cpu time''': 45.0 Seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
Predicted change in Energy=-2.577712D-08
Optimization completed.
-- Stationary point found.
</pre>

==== Energy and structure comparison ====
{| class="wikitable" border="1"
! !! HF 3-21G !! DFT 6-31G*
|-
! Point group
| Ci || Ci
|-
! Energy/HF
| -231.693 || -234.612
|-
! Relative Energy/kJmol-1
| 7664.3 || 0
|}

The energy from the B3LYP/6-31G* calculation is much lower than that from the HF/3-21G, however the structure is the same and retains the same symmetry. This shows that both levels of theory give the correct optimised structure but the higher level of theory gives a lower energy which is closer to the actual energy of the molecule in its optimised state.

===Optimising the 'chair' and 'boat' transition structures===
====Chair TS====
'''Allyl fragment optimisation''' 
[[File:Vm1110_allyl_opt.png|300px]] 
[[File:Vm1110_allyl_opt.log]] 
[[File:Vm1110_allyl_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': UHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -115.82303985 au 
'''RMS Gradient Norm''': 0.00008192 au 
'''Dipole Moment''': 0.0294 Debye 
'''Point Group''': C2 
'''Job cpu time''': 5.0 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000388 0.001200 YES
Predicted change in Energy=-2.083720D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Chair TS opt+freq''' 
Two fragments were arranged such that the central C atoms on each fragment were point outwards, away from one another, forming the chair transition state. The transition state was found and optimised by using the opt+freq job type, the Hartree Frock method and the 3-21G basis set. 
[[File:Vm1110_chair_opt.gif|300px]] 
(Click the enlarge and see vibration) 
[[File:Vm1110_chair_opt.log]] 
[[File:Vm1110_chair_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.61932241 au 
'''RMS Gradient Norm''': 0.00008192 au 
'''Dipole Moment''': 0.0006 Debye 
'''Point Group''': C1 
'''Job cpu time''': 19.0 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001795 0.001800 YES
RMS Displacement 0.000458 0.001200 YES
Predicted change in Energy=-6.233796D-08
Optimization completed.
-- Stationary point found.
</pre>
The imaginary frequency shown in the above image for the transition state occurs at -818cm-1 and shows the bond formation in the transition state. 
====Boat TS====
The boat transition state was optimised by using the optimised ''anti2'' conformer of 1,5-hexadiene and performing an opt+freq calculation using QST2 method. The first attempt with the optimised conformer with no alternations failed so the dihedral angle of the central C-C bond was rotated by 180° so that the molecules more closely resembled the boat transition state and could be more easily optimised. 
'''Failed Boast TS optimisation''' 
[[File:Vm1110_boat_opt_failed.log]] 
[[File:Vm1110_boat_opt_failed.chk]] 
'''Successful Boast TS optimisation''' 
[[File:Vm1110_boat_opt.gif|300px]] 
(Click the enlarge and see vibration) 
[[File:Vm1110_boat_opt.log]] 
[[File:Vm1110_boat_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.60280239 au 
'''RMS Gradient Norm''': 0.00003250 au 
'''Dipole Moment''': 0.1584 Debye 
'''Point Group''': CS 
'''Job cpu time''': 29.0 
The imaginary frequency shown in the above image for the transition state occurs at -840cm-1 and shows the bond formation in the transition state. 

==== IRC ====
An IRC calculation was performed on the optimised chair transition structure to confirm that the transition state was a maximum energy.
'''IRC''' 
[[File:Vm1110_chair_irc..png|400px]] 
[[File:Vm1110_chair_irc.log]] 
(checkpoint file too large to upload to wiki) 
'''File Type''': .log 
'''Calculation Type''': IRC 
'''Calculation Method''': 
'''Basis Set''': 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.61932241 au 
'''RMS Gradient Norm''': 0.00001799 au 
'''Dipole Moment''': 0.0006 Debye 
'''Point Group''': C1 
'''Job cpu time''': 16 minutes 38.0 seconds 
The graph above shows that the transition state found does indeed occupy the highest energy, hence it is the transition state. The IRC was calculated only in the forward direction because for this molecule it is symmetric. 

==== Activation Energies ====

==Part 2: Diels Alder==

=== Cis butadiene optimisation===
[[File:Vm1110_butadiene_opt.png|300px]]
==== Optimisation file ====
[[File:Vm1110_butadiene_opt.log]] 
[[File:Vm1110_butadiene_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': 0.04879719 au 
'''RMS Gradient Norm''': 0.00001742 au 
'''Dipole Moment''': 0.0414 Debye 
'''Point Group''': C2V 
'''Job cpu time''': 2.0 seconds 
==== Item table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000442 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-8.983482D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Molecular Orbitals ====

{| class="wikitable" border="1"
! !! HOMO !! LUMO
|-
!Orbital
|[[File:Vm1110_butadiene_HOMO.png|200px]] || [[File:Vm1110_butadiene_LUMO.png|200px]]
|-
! Symmetry
| Asymmetric || Symmetric
|}

 
=== Prototype reaction transition state ===

The transition state was investigated for the following reaction: 
[[File:Mb_da3.jpg|300px]] 
The correct geometry was found by drawing and cleaning up the bicyclo structure and removing one of the added ethylene fragments. The transition state was optimised and characterised using the opt+freq job type. The method used was semi-empirical AM1, as for the optimisation above.
==== Optimisation/frequency file ====
[[File:vm1110_prototype_ts.gif|300px]] 
[[File:Vm1110_prototype_ts.log]] 
[[File:Vm1110_prototype_ts.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': 0.11165464 au 
'''RMS Gradient Norm''': 0.00000030 au 
'''Dipole Moment''': 0.5605 Debye 
'''Point Group''': C1 
'''Job cpu time''': 3.0 seconds 
==== Item table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000028 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-9.870468D-12
Optimization completed.
-- Stationary point found.
</pre>

'''HOMO''' 
[[File:vm1110_prototype_HOMO.png|300px]] 
Asymmetric. Formed from the HOMO of the cis butadiene (AS, as seen above)) and the LUMO of the -CH2-CH2- fragment.
 

==== Discussion ====

The optimisation converged and the frequency file gave a single imaginary vibration at -956cm-1 corresponding to the bond formation. The frequency also gave thermochemical information about the transition state, shown below.
<pre>
Sum of electronic and zero-point Energies= 0.253276
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015
</pre>
 
=== Diels Alder reaction with maleic anhydride ===

Maleic anhydride reacts with cyclohexa-1,3-diene in a diels alder mechanism to give an endo and an exo product. The reaction is kinetically controlled. Below the energies of the transition states for both the endo and the exo forms are compared.
==== Endo transition state ====
[[File:vm1110_endo_ts.gif|300px]] 
'''Optimisation''' 
[[File:Vm1110_endo_ts.log]] 
[[File:Vm1110_endo_ts.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -0.05150480 au 
'''RMS Gradient Norm''': 0.00000027 au 
'''Dipole Moment''': 0.5605 Debye 
'''Point Group''': C1 
'''Job cpu time''': 5.0 seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-5.113571D-12
Optimization completed.
-- Stationary point found.
</pre>
==== Exo transition state ====
[[File:vm1110_exo_ts.gif|300px]] 
'''Optimisation''' 
[[File:Vm1110_exo_ts.log]] 
[[File:Vm1110_exo_ts.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''':-0.05041968 au 
'''RMS Gradient Norm''': 0.00004220 au 
'''Dipole Moment''': 5.5647 Debye 
'''Point Group''': C1 
'''Job cpu time''': 11.0 seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001782 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-1.720725D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Discussion ====

{| class="wikitable" border="1"
|+ Molecular Orbitals
!
! colspan="2" | Endo
! colspan="2" | Exo
|-
! MOs
| [[File:vm1110_endo_homo.gif|150px]] HOMO || [[File:vm1110_endo_lumo.gif|150px]] LUMO ||[[File:vm1110_exo_homo.gif|150px]] HOMO || [[File:vm1110_exo_lumo.gif|150px]] LUMO
|}
As can be seen in the above table, the central oxygen on the maleic anhydride contributes less to the overall bonding and antibonding of the LUMO and HOMO for the exo product than the endo product. This is due to oxygen being highly electronegative.

{| class="wikitable" border="1"
|+ C-C distances
!
! Endo
! Exo
|-
! partially formed σ C-C bond
| 2.162 || 2.170
|-
! C-C through space distances
| 2.892 || 2.945
|-
! C-C single bond in cyclohexa-1,3-diene
| 1.393 || 1.394
|-
! C-C single bond in maleic anhydride
| 1.489 || 1.488
|}
The carbon Van der Waal radius of carbon is 1.7, compared to this the C-C distance through space is much shorter than the sum of two carbon Van der Waal radii. This means that there are forces holding the carbons closer together. This is due to secondary orbital overlap effect. This is more pronounced for the endo transition state which explains why it is lower in energy. 

{| class="wikitable" border="1"
|+ Relative energies
! !! Endo !! Exo
|-
! Energy/HF
| -0.052 || -0.050
|-
! Relative Energy/kJmol-1
| 0 || 2.849
|}
These relative energies show that the endo form is lower in energy and therefore more stabilised.

Rep:Mod:seaunicorn13

2012-12-07T19:43:38Z

Vm1110: /* Discussion */

==Part 1: Cope Rearrangement==

===Optimising the reactants and products===

The following conformers of 1,5-hexadiene were drawn and optimised in GaussView, the given names correspond to those given in [[mod:phys3#Appendix_1|appendix 1]].
{| class="wikitable" border="1"
! Conformer
! ''Gauche1'' !! ''Gauche3'' !! ''Anti1'' !!
''Anti2''
|-
! Structure
| [[FILE:vm1110_hexadiene_gauche_1.png| 200px]] ||[[FILE:vm1110_hexadiene_gauche_3.png| 200px]]||[[FILE:vm1110_hexadiene_anti_1.png| 200px]]||[[FILE:vm1110_hexadiene_anti_2.png| 200px]]
|-
! Point Group
| C1||C1||C2||Ci
|-
! Energy/Hartree
| -231.688 || -231.693 || -231.693 || -231.693
|-
! Relative energy/kJmol-1
| 13.0||0||0.2||0.3
|-
! File link
| [[FILE:vm1110_hexadiene_gauche_1.log]]||[[FILE:vm1110_hexadiene_gauche_3.log]]|| [[FILE:vm1110_hexadiene_anti_1.log]]||[[FILE:vm1110_hexadiene_anti_2.log]]
|-
! File Summary
| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.68771617 au 
'''RMS Gradient Norm''': 0.00000295 au 
'''Dipole Moment''': 0.4554 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69266122 au 
'''RMS Gradient Norm''': 0.00000478 au 
'''Dipole Moment''': 0.3405 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69260236 au 
'''RMS Gradient Norm''': 0.00000559 au 
'''Dipole Moment''': 0.2021 Debye 
'''Job cpu time''': 7.0 Seconds 

| '''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.69253516 au 
'''RMS Gradient Norm''': 0.00004316 au 
'''Dipole Moment''': 0.000 Debye 
'''Job cpu time''': 5.0 Seconds 
|}
The energies obtained correspond to those given in [[mod:phys3#appendix_1|appendix 1]].

===Anti2 optimisation===

The anti2 conformer was optimised to a higher level of theory.

'''Optimisation file''' 
[[File:Vm1110_anti2_opt_631.log]] 
[[File:Vm1110_anti2_opt_631.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RB3LYP 
'''Basis Set''': 6-31G(d) 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -234.61171020 au 
'''RMS Gradient Norm''': 0.00001448 au 
'''Dipole Moment''': 0 Debye 
'''Point Group''': Ci 
'''Job cpu time''': 45.0 Seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000021 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000747 0.001800 YES
RMS Displacement 0.000252 0.001200 YES
Predicted change in Energy=-2.577712D-08
Optimization completed.
-- Stationary point found.
</pre>

==== Energy and structure comparison ====
{| class="wikitable" border="1"
! !! HF 3-21G !! DFT 6-31G*
|-
! Point group
| Ci || Ci
|-
! Energy/HF
| -231.693 || -234.612
|-
! Relative Energy/kJmol-1
| 7664.3 || 0
|}

The energy from the B3LYP/6-31G* calculation is much lower than that from the HF/3-21G, however the structure is the same and retains the same symmetry. This shows that both levels of theory give the correct optimised structure but the higher level of theory gives a lower energy which is closer to the actual energy of the molecule in its optimised state.

===Optimising the 'chair' and 'boat' transition structures===
====Chair TS====
'''Allyl fragment optimisation''' 
[[File:Vm1110_allyl_opt.png|300px]] 
[[File:Vm1110_allyl_opt.log]] 
[[File:Vm1110_allyl_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': UHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -115.82303985 au 
'''RMS Gradient Norm''': 0.00008192 au 
'''Dipole Moment''': 0.0294 Debye 
'''Point Group''': C2 
'''Job cpu time''': 5.0 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000139 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001133 0.001800 YES
RMS Displacement 0.000388 0.001200 YES
Predicted change in Energy=-2.083720D-07
Optimization completed.
-- Stationary point found.
</pre>

'''Chair TS opt+freq''' 
Two fragments were arranged such that the central C atoms on each fragment were point outwards, away from one another, forming the chair transition state. The transition state was found and optimised by using the opt+freq job type, the Hartree Frock method and the 3-21G basis set. 
[[File:Vm1110_chair_opt.gif|300px]] 
(Click the enlarge and see vibration) 
[[File:Vm1110_chair_opt.log]] 
[[File:Vm1110_chair_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.61932241 au 
'''RMS Gradient Norm''': 0.00008192 au 
'''Dipole Moment''': 0.0006 Debye 
'''Point Group''': C1 
'''Job cpu time''': 19.0 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000051 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.001795 0.001800 YES
RMS Displacement 0.000458 0.001200 YES
Predicted change in Energy=-6.233796D-08
Optimization completed.
-- Stationary point found.
</pre>
The imaginary frequency shown in the above image for the transition state occurs at -818cm-1 and shows the bond formation in the transition state. 
====Boat TS====
The boat transition state was optimised by using the optimised ''anti2'' conformer of 1,5-hexadiene and performing an opt+freq calculation using QST2 method. The first attempt with the optimised conformer with no alternations failed so the dihedral angle of the central C-C bond was rotated by 180° so that the molecules more closely resembled the boat transition state and could be more easily optimised. 
'''Failed Boast TS optimisation''' 
[[File:Vm1110_boat_opt_failed.log]] 
[[File:Vm1110_boat_opt_failed.chk]] 
'''Successful Boast TS optimisation''' 
[[File:Vm1110_boat_opt.gif|300px]] 
(Click the enlarge and see vibration) 
[[File:Vm1110_boat_opt.log]] 
[[File:Vm1110_boat_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RHF 
'''Basis Set''': 3-21G 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.60280239 au 
'''RMS Gradient Norm''': 0.00003250 au 
'''Dipole Moment''': 0.1584 Debye 
'''Point Group''': CS 
'''Job cpu time''': 29.0 
The imaginary frequency shown in the above image for the transition state occurs at -840cm-1 and shows the bond formation in the transition state. 

==== IRC ====
An IRC calculation was performed on the optimised chair transition structure to confirm that the transition state was a maximum energy.
'''IRC''' 
[[File:Vm1110_chair_irc..png|400px]] 
[[File:Vm1110_chair_irc.log]] 
(checkpoint file too large to upload to wiki) 
'''File Type''': .log 
'''Calculation Type''': IRC 
'''Calculation Method''': 
'''Basis Set''': 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -231.61932241 au 
'''RMS Gradient Norm''': 0.00001799 au 
'''Dipole Moment''': 0.0006 Debye 
'''Point Group''': C1 
'''Job cpu time''': 16 minutes 38.0 seconds 
The graph above shows that the transition state found does indeed occupy the highest energy, hence it is the transition state. The IRC was calculated only in the forward direction because for this molecule it is symmetric. 

==== Activation Energies ====

==Part 2: Diels Alder==

=== Cis butadiene optimisation===
[[File:Vm1110_butadiene_opt.png|300px]]
==== Optimisation file ====
[[File:Vm1110_butadiene_opt.log]] 
[[File:Vm1110_butadiene_opt.chk]] 
'''File Type''': .log 
'''Calculation Type''': FOPT 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': 0.04879719 au 
'''RMS Gradient Norm''': 0.00001742 au 
'''Dipole Moment''': 0.0414 Debye 
'''Point Group''': C2V 
'''Job cpu time''': 2.0 seconds 
==== Item table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000030 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000442 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-8.983482D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Molecular Orbitals ====

{| class="wikitable" border="1"
! !! HOMO !! LUMO
|-
!Orbital
|[[File:Vm1110_butadiene_HOMO.png|200px]] || [[File:Vm1110_butadiene_LUMO.png|200px]]
|-
! Symmetry
| Asymmetric || Symmetric
|}

 
=== Prototype reaction transition state ===

The transition state was investigated for the following reaction: 
[[File:Mb_da3.jpg|300px]] 
The correct geometry was found by drawing and cleaning up the bicyclo structure and removing one of the added ethylene fragments. The transition state was optimised and characterised using the opt+freq job type. The method used was semi-empirical AM1, as for the optimisation above.
==== Optimisation/frequency file ====
[[File:vm1110_prototype_ts.gif|300px]] 
[[File:Vm1110_prototype_ts.log]] 
[[File:Vm1110_prototype_ts.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': 0.11165464 au 
'''RMS Gradient Norm''': 0.00000030 au 
'''Dipole Moment''': 0.5605 Debye 
'''Point Group''': C1 
'''Job cpu time''': 3.0 seconds 
==== Item table ====
<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000028 0.001800 YES
RMS Displacement 0.000006 0.001200 YES
Predicted change in Energy=-9.870468D-12
Optimization completed.
-- Stationary point found.
</pre>

'''HOMO''' 
[[File:vm1110_prototype_HOMO.png|300px]] 
Asymmetric. Formed from the HOMO of the cis butadiene (AS, as seen above)) and the LUMO of the -CH2-CH2- fragment.
 

==== Discussion ====

The optimisation converged and the frequency file gave a single imaginary vibration at -956cm-1 corresponding to the bond formation. The frequency also gave thermochemical information about the transition state, shown below.
<pre>
Sum of electronic and zero-point Energies= 0.253276
Sum of electronic and thermal Energies= 0.259453
Sum of electronic and thermal Enthalpies= 0.260397
Sum of electronic and thermal Free Energies= 0.224015
</pre>
 
=== Diels Alder reaction with maleic anhydride ===

Maleic anhydride reacts with cyclohexa-1,3-diene in a diels alder mechanism to give an endo and an exo product. The reaction is kinetically controlled. Below the energies of the transition states for both the endo and the exo forms are compared.
==== Endo transition state ====
[[File:vm1110_endo_ts.gif|300px]] 
'''Optimisation''' 
[[File:Vm1110_endo_ts.log]] 
[[File:Vm1110_endo_ts.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''': -0.05150480 au 
'''RMS Gradient Norm''': 0.00000027 au 
'''Dipole Moment''': 0.5605 Debye 
'''Point Group''': C1 
'''Job cpu time''': 5.0 seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000023 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
Predicted change in Energy=-5.113571D-12
Optimization completed.
-- Stationary point found.
</pre>
==== Exo transition state ====
[[File:vm1110_exo_ts.gif|300px]] 
'''Optimisation''' 
[[File:Vm1110_exo_ts.log]] 
[[File:Vm1110_exo_ts.chk]] 
'''File Type''': .log 
'''Calculation Type''': FREQ 
'''Calculation Method''': RAM1 
'''Basis Set''': ZDO 
'''Charge''': 0 
'''Spin''': Singlet 
'''E(RB3LYP)''':-0.05041968 au 
'''RMS Gradient Norm''': 0.00004220 au 
'''Dipole Moment''': 5.5647 Debye 
'''Point Group''': C1 
'''Job cpu time''': 11.0 seconds 
'''Item table''' 
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001782 0.001800 YES
RMS Displacement 0.000188 0.001200 YES
Predicted change in Energy=-1.720725D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Discussion ====

{| class="wikitable" border="1"
|+ Molecular Orbitals
!
! colspan="2" | Endo
! colspan="2" | Exo
|-
! MOs
| [[File:vm1110_endo_homo.gif|200px]] HOMO || [[File:vm1110_endo_lumo.gif|200px]] LUMO ||[[File:vm1110_exo_homo.gif|200px]] HOMO || [[File:vm1110_exo_lumo.gif|200px]] LUMO
|}
As can be seen in the above table, the central oxygen on the maleic anhydride contributes less to the overall bonding and antibonding of the LUMO and HOMO for the exo product than the endo product. This is due to oxygen being highly electronegative.

{| class="wikitable" border="1"
|+ C-C distances
!
! Endo
! Exo
|-
! partially formed σ C-C bond
| 2.162 || 2.170
|-
! C-C through space distances
| 2.892 || 2.945
|-
! C-C single bond in cyclohexa-1,3-diene
| 1.393 || 1.394
|-
! C-C single bond in maleic anhydride
| 1.489 || 1.488
|}
The carbon Van der Waal radius of carbon is 1.7, compared to this the C-C distance through space is much shorter than the sum of two carbon Van der Waal radii. This means that there are forces holding the carbons closer together. This is due to secondary orbital overlap effect. This is more pronounced for the endo transition state which explains why it is lower in energy.

Rep:Mod:seaunicorn13

2012-12-07T19:15:36Z