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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 appendix 1.

Conformer Gauche1 Gauche3 Anti1

Anti2

Structure
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 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

         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.

Energy and structure comparison

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.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

         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.

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.

(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

         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.

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

(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.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)

HF 3-21G 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)

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

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

         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.

Molecular Orbitals

HOMO LUMO
Orbital
Symmetry Asymmetric Symmetric


Prototype reaction transition state

The transition state was investigated for the following reaction:

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.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

         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.

HOMO

Asymmetric. Formed from the HOMO of the cis butadiene (AS, as seen above)) and the LUMO of the -CH2-CH2- fragment.
LUMO

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.

 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


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


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

         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.

Exo transition state


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

         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.

Discussion

Molecular Orbitals
Endo Exo
MOs
HOMO

LUMO

HOMO

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.

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.

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.