Rep:Mod:ickm1330

Module 3: Transition States and Reactivity

The Cope Rearrangement

The Cope rearrangement is the [3,3]-sigmatropic shift seen in 1,5-dienes, and is named after Arthur C. Cope who initially observed the process .

Since its discovery, much study has been devoted to the Cope rearrangement and it now accepted to proceed in a concerted fashion either via a chair or via a boat transition state. In this section, computational methods will be used to model each of these transition states, and from the models activation energies and enthalpies will be derived.

Optimising Reactants and Products

Gaussview was used to construct both a “gauche” and “anti” conformer of 1,5-hexadiene. These structures were then optimised under HF/3-21G.

Structure	Illustration	Symmetry	Energy (HF/3-21G) / Ha
Anti		C2	-231.692602
Gauche		C1	-231.692661

Although the difference is slight, the gauche conformer is seen to be slightly higher in energy than the anti conformer. This is likely due to steric interactions between the carbon branches when gauche to one another.

The anti conformer was then altered in an attempt to minimise energy. To reduce all steric interactions the C=C groups were positioned with a 180 ° dihedral angle about the central C-C bond.

However, upon optimisation under HF/3-21G, this structure returns to the C2 anti conformation with an energy of -231.692602 Ha.

The anti2 conformer was also constructed. Upon optimisation under HF/3-21G it had an energy of -231.692535 Ha and C_i symmetry. The optimised anti2 was then resubmitted for optimisation under the B3LYP/6-31G(d) level of theory.

Slight changes in geometry were noted after optimisation at a higher level of theory:

bonds	dihedral (HF)	dihedral (DFT)
guache C-H bonds on central Cs
C=C with central C-C

Frequency analysis was also performed on the anti2 conformer at the B3LYP/6-31G(d) level. The highest "low frequency" was seen at -16cm^-1, and other than this no other imaginary frequencies were seen, indicating that a minimum geometry had indeed been achieved.

Thermochemical information was obtained through the frequency analysis.

Result	Value at 298.15K	Value at 1K
sum of electronic and zero-point energies	-234.469189	-234.468752
sum of electronic and thermal energies	-234.461840	-234.468742
sum of electronic and thermal enthalpies	-234.460896	-234.468739
sum of electronic and thermal free energies	-234.500775	-234.468772

Optimising Transition States

Chair Transition

Two similar methods were used for the optimisation of the chair transition state. The transition state can be thought of as two "allyl fragments" arranged in a chair formation. So to begin, the structure of the allyl fragment is determined. The fragments were drawn is GaussView, and optimised using HF/3-21G.

A guess structure for the chair transition state was then created, with two optimised allyl fragments arranged in the chair formation, with a spacing of 2.2 Å between the atoms were σ bonds are created or destroyed.

The first of the two methods was the use of the TS(Berny) algorithm. An optimisation with frequency analysis was performed on the guessed transition structure, with the optimisation being directed to a transition state, rather than a minimum using the HF/3-21G level of theory.

The optimised structure had a single imaginary frequency, at -818cm^-1, showing that a transition state had been reached. This corresponded to the Cope reaction, with the bond formation and destruction occurring in a concerted manner.

The second method involves pre-optimising the structures of the transition state with the reaction coordinate frozen, to obtain a better guess structure, and then performing a second optimisation with the reaction coordinate unfrozen to determine the transition state structure.

Again calculations were performed at the HF/3-21G level of theory. The imaginary frequency at -818cm^-1 is also seen using this method. A comparison of the bond lengths obtained allows the methods to be compared.

Bond	Length / Å
	TS(Berny)	Frozen Coordinate
C-C within allyl fragment
C-C between allyl fragments

As the resulting geometries from each method are very similar, it is likely that the methods are approximately equivalent in this situation.

Boat Transition

Another alternative method is used to arrive at the boat transition state. The QST2 method, which works out the structure by determining the intermediate between the reactant and product structures.

The anti2 structure was set up as both reactant and product of the Cope rearrangement reaction, with the atoms suitably labelled so the reactant and product correlated. This was submitted for optimisation using the QST2 method under HF/3-21G.

This however did not yield the boat transition state. Instead the job failed, and finished in a structure similar to the chair transition state.Thus to allow the boat transition state to form, the conformations of the reactants and products were suitably altered.

Reactant	Product

Optimisation using QST2 with HF/3-21G produced the boat transition state. The C-C lengths for the carbons the allyl groups and the allyl groups were 1.38135 Å 2.140 Å respectively. The allyl C-C bonds are slightly shorter in this case, compared to the chair TS, while the bond being made/broken are slightly longer in the transition state in the boat TS.

Frequency analysis was also performed on the boat transition state, and one was obtained at 839cm^-1. The vibration itself matches the Cope rearrangement.

The Diels-Alder Reaction

The Diels-Alder reaction, first documented in 1928, is a key example of a [4+2] cycloaddition and is a crucial reaction in modern synthesis. The reaction involves the addition of a substituted alkene to a diene to form a structure based on cyclohexene. The mechanism for the reaction involves the concerted formation of two new σ bonds, and is highly dependant on the interaction of the π orbitals of the alkene and and diene.

The Prototype Reaction

The two most simple structures available to take place in a Diels-Aldr cyclisation are butadiene and ethene. This simplified system allows for a clear view of the behaviour of the molecular orbitals as a cyclisation proceeds.

The reaction can be analysed through a series of gaussian calculations to gain an insight into the mechanism.

Butadiene Optimisation

To begin the reactant butadiene molecule was constructed using gaussian, and optimised using the semi-empirical AM1 level of theory. Cubegen was then used to visualise the highest occupied and lowest unoccupied molecular orbitals for the molecule.

The HOMO of butadiene is antisymmetric with respect to the C_2v plane through the molecule, while the LUMO is symmetric with respect to the C_2v plane.

Prototype Transition

transition state structure

In order to determine the structure of the transition state for this reaction, the QST2 method with the semi-empirical AM1 level of theory, was used to interpolate between the preoptimised butadiene and ethene reaction combination and the cyclohexene product. Frequency analysis was performed and a single imaginary frequency was seen at -956cm^-1.

bond lengths in the transition structure

Bond	Length / &Aring	Bond	Length / Å

Comparatively, a typical sp³ bond distance is 1.514 Å, a typical sp² double bond is 1.317 Å and the Van der Waals radius of carbon is 1.70 &Aring . All of the intermolecular bonds are slightly longer than a double bond, but significantly shorter than a single bond, showing that a large amount of π character is present.

The bond distances between the diene and the alkene however are much longer than even the single bond. But the length is much shorter than the combined Van der Waal radii of the two carbons (3.40 Å), suggesting that some degree of bonding is taking place.

Looking at the molecular orbitals, bonding in the transition state is more evident. The HOMO is antisymmetric with regards to the C_2v plane of symmetry. The HOMO of butadiene can be seen to interact with the π* orbital on the ethene. Clear areas of overlap occur indicative of σ bonds forming between the terminal carbons on the butadiene and the carbons on the ethene. The LUMO on the other hand is formed through the interaction of the butadiene LUMO and the ethene π orbital and is symmetric in the C_{2v plane.}

HOMO	LUMO

Diels-Alder with Substituted Reactants

Reactant Optimisation

Maleic Anhydride
Cyclohexa-1,3-diene

Transition Optimisation

Transition	HOMO	LUMO	Transition Energy