Rep:Mod:imgettingAlder

The Diels Alder Cycloaddition

Here, the methods used previously will be applied to Diels Alder reactions. Diels Alder reactions are pericyclic and are concerted. A dieneophile interact with a diene to form σ bonds from pi bonds. The interaction of the HOMO/LUMO of the interacting species depends if the reaction is allowed or forbidden. If the HOMO of one species can interact with the LUMO of the other, the reaction is allowed. There must be significant overlap and the same symmetry. If there are substituents with π orbitals that are of the correct symmetry to interact with the π orbitals, then this can favour a particular position of attack.

Cis-butadiene and Ethylene

To start, the reactants were optimised using the AM1 semi-empirical molecular orbital method. The HOMO and LUMO of both were calculated and are shown. Ethylene is the dieneophile and cis-butadiene is the diene.

Table 9: Molecular Orbitals of Cis-butadiene and Ethylene

Molecule	Molecular Orbital	Molecular Orbital Diagram	Symmetry	Energy/ Hartrees
Cis-butadiene	LUMO		Symmetric	0.01796
Link to file: Media:danCISBUTADIENE-OPT.LOG	HOMO		Anti-symmetric	-0.34455
Ethylene	LUMO		Anti-symmetric	0.05284
Link to file: Media:danETHYLENE.LOG	HOMO		Symmetric	-0.38777

Looking at the symmetry on the MO’s we can see that the LUMO of cis-butadiene can interact with the HOMO ethylene. Therefore, this reaction is allowed. The other set of HOMO and LUMO also match but these are not π orbitals.

I calculated the transition state using the ‘Frozen coordinate’ method used earlier with the AM1 semi-empirical molecular orbital method, then this I optimised this to a higher accuracy using the B3LYP/6-31G and the following information was produced.

Table 10: Transition state of Cis-butadiene and Ethylene

Diagram
Energy/ Hartrees	-234.495
Link to file	Media:TRANSDIELSALDER1-FROZEN-6-31GDAN.LOG
Imaginary Frequency/ cm-1	-534
Imaginary Frequnecy Diagram

The imaginary frequency clearly shows the concerted formation of the bonds, which is as expected. Let’s examine the HOMO and LUMO.

Table 11: Molecular Orbitals of Transition State

Molecule	Molecular Orbital	Molecular Orbital Diagram	Symmetry	Energy/ Hartrees
Transition State	LUMO	[[Image:|200px]]	Symmetric
	HOMO	[[Image:|200px]]	Anti-symmetric

If we calculate the energy of the optimised product we can work out the activation energy. The energy of the product is Link to file: [[Media:]]

Table 12: Activation Energies

Activation Energy/ Hartrees	Activation Energy/ kcal/mol

The value obtained is consistent with the literature value 115 KJ mol^-1 but there is a difference and this does show that Gaussian calculation are not 100% qualitative but do give a very good approximation which was also seen earlier.

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Cyclohexa-1,3-diene and Maleic Anhydride

(show reaction)

This reaction has two possible products and here we will discuss the region selectivity. The C=O bond has pi orbitals which can interact to stabilise a particular transition state. This will be shown by analysing the two possible transition states. The transition states were found using the ‘frozen coordinate’ method with the semi-empirical/AM1 method.

Again, the imaginary frequencies show the concerted bond formation nicely. We can see that the endo transition state has a lower energy than the exo transition state. If we draw the Frontier Orbitals, we can see that the endo transition state has some interaction from the C=O pi orbitals, which stablise the transition state, hence lowering its energy.

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References