The Cope rearrangement of 1,5-hexadiene is a typical [3,3]sigmatropic rearrangement. The mechanism of this reaction is generally believe to go trough 'chair' and 'boat' transition state(TS). During the tutorial, we built both transition structure and found their activation energies.
Cope rearrangement
Reactants
Conformer
Structure
Point Group
Energy/Hartrees HF/3-21G
Relative Energy/kcal/mol
gauche3
C1
-231.692660
0.00
anti2
Ci
-231.69253529
0.08
anti3
C2h
-231.689069999
2.25
Chair and Boat Transition Structure
Chair Transition Structure
Imaginary Frquency of chair TS
Boat Transition Structure
Imaginary Frquency of boat TS
QTS2 is used to generated to transition structure form the structure of reactant and product. The numbering of atomic from atomic list must be keep the same order.
Intrinsic Reaction Coordinate
IRC for the reaction
Energy plot for the IRC
In this case, IRC is only running in one direction as the reaction is symmetric and the other direction will be exactly the same. Where as for the reaction is not symmetric, it is necessary to run the IRC in both direction(which is used in later past of this wiki page).
At 298.15K
Chair-TS
Boat-TS
HF/3-21G
B3LYP/6-31G*
HF/3-21G
B3LYP/6-31G*
Sum of electronic and zero-point Energies
-231.466714
-234.411655
-234.391626
-234.427323
Sum of electronic and thermal Energies
-231.461353
-234.405192
-231.450922
-234.392570
Sum of electronic and thermal Enthalpies
-231.602802
-234.441291
-231.444349
-234.396006
Sum of electronic and thermal Free Energies
-231.495222
-231.466714
-231.479768
-234.461856
At 0K
Chair-TS
Boat-TS
HF/3-21G
B3LYP/6-31G*
HF/3-21G
B3LYP/6-31G*
Sum of electronic and zero-point Energies
-231.466714
-234.411655
-231.450922
-234.398496
Sum of electronic and thermal Energies
-231.466714
-234.411655
-231.450922
-234.398496
Sum of electronic and thermal Enthalpies
-231.466714
-234.411655
-231.450922
-234.398496
Sum of electronic and thermal Free Energies
-231.466714
-234.411655
-231.450922
-234.398496
HF/3-21G
B3LYP/6-31G*
Electronic energy
Sum of electronic and zero-point energies
Sum of electronic and thermal energies
Electronic energy
Sum of electronic and zero-point energies
Sum of electronic and thermal energies
at 0 K
at 298.15 K
at 0 K
at 298.15 K
Chair TS
-231.466714
-231.466714
-231.461353
-234.54046002
-234.411655
-234.405192
Boat TS
-231.60280239
-231.450922
-231.445294
-234.54046002
-234.398497
-234.392570
Reactant (anti2)
-231.692535
-231.539539
-231.532566
-234.611710
-234.469203
-234.461856
Summary of activation energies (in kcal/mol)
HF/3-21G
HF/3-21G
B3LYP/6-31G*
B3LYP/6-31G*
Expt.
at 0 K
at 298.15 K
at 0 K
at 298.15 K
at 0 K
ΔE (Chair)
45.70
44.69
36.11
34.93
33.5 ± 0.5
ΔE (Boat)
55.61
54.76
44.37
43.48
44.7 ± 2.0
From the Activation energies that calculated above, the HF/21G optimisation result is less actuate than 6-31G* as the activation energy generated from 6-31G* is way closer in both case.
The Diels Aider Cycloaddition
Cis-butadiene and Ethene
HOMO
LUMO
butadiene
ethene
(The butadiene structure in the figures above does not seem to be in a planar configuration, C2v, is that what you expected?João (talk) 12:30, 12 February 2015 (UTC))
As shown in the graph above, the HOMO and LUMO of cis-butadiene are both symmetrical to the mirror plane. The HOMO transition state is generate from LUMO of butadiene (S)and HOMO ethene(S). The LUMO of TS is generated from LUMO (S)of ditadiene and LUMO+1(AS). It is worth noticing that AS and S can generate symmetrical MO.
(What is the overlap integral of a symmetric and an anti-symmetric orbital? Can they interact?João (talk) 12:30, 12 February 2015 (UTC))
Imaginary Frquency of TS
HOMO of TS
LUMO of TS
Endo vs Exo Diels-Alder Reaction
Exo TS Imagery frequency
Endo TS Imagery frequency
Exo product
IRC of Exo product
Energy plot of IRC
Endo Product
IRC of Endo product
Energy plot of Endo IRC
electronic energy of starting point(hartree)
electronic energy of TS(hartree)
ΔE(hartree)
exo
-605.651
-605.610
0.041
endo
-605.652
-605.604
0.048
activation energy to TS
kcal/mol
exo
30.12
endo
25.73
The ICR calculation coverage backward to a local minimum on the both energy plot. Theoretically the backward reaction should not be converge as the reactants will have the minimum energy at infinity. This case we assume it is the energy of reactant as the molecule will approach to each other during the reaction. The different in energy of reactant and transition state is the activation energy.The calculation indicate that exo transition structure have a higher energy transition state(4.39 kcal/mol more than endo). As we know the reaction is driven by kinetics (Doesn't this depend on reaction conditions? What happens at high temperatures?João (talk) 12:30, 12 February 2015 (UTC)), the major product will endo-prodoct as it has a lower energy transition state.
Endo
Exo
LUMO
HOMO
From the molecular orbital of Endo and Exo TS, It is important to see that in the HOMO of Endo-TS the Π orbital on oxygen in -(C=O)-O-(C=O)- fragment can interact and donating electron to the Π* orbital of conjugate double bond orbital in cyclohexa-1,3-diene shown in the LUMO of Exo-TS. This orbital contribution will lower down the overall electronic energy of Endo-TS. This secondary orbital overlap effect is consider to be the main contribution to the lower energy Transition state of endo-product. Where as for the Exo-Ts, there is effect is hard to observe.
