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Module3:Transition states and reactivity

The Cope Rearrangement of 1,5-hexadiene

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.

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, C_2v, 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

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IRC of Exo product	Energy plot of IRC

Endo Product

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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.