Jump to content

Rep:Mod3:Yuko.Isayama3001Ex2

From ChemWiki

The Diels Alder Cycloaddition

In a Diel-Alder reaction, the π orbitals of the dienophile combine with the π orbitals of the diene to form new σ bonds. The number of π electrons involved determine whether or not the reaction occurs in a concerted stereospecific fashion (allowed) or not (forbidden). Generally the HOMO/LUMO of one reactant interacts with the HOMO/LUMO of the other to form two new bonding/antibonding MOs.

If the dienophile is substituted, with substituents that have π orbitals, they can stabilise the regiochemistry of the reaction by interacting with new double bond that has been formed.

In this section, the transition structures for the Diels-Alder reactions between ethylene and cis-butadiene which is a prototypical reaction, and between that of cyclohexa-1,3-diene and maleic anhydride, where both reactants carry substituents were characterised by the frozen coordinate method, followed by examining the molecular orbitals. For all the calculations the AM1 semi-empirical molecular orbital was used.

Ethylene and Cis-Butadiene

Diels-Alder reaction between ethylene and cis-butadiene

Optimisation and Molecular Orbitals of Cis-Butadiene and Ethylene

Optimisation of cis-butadiene and ethylene based on the AM1 semi-empricial orbital method gave energies of 0.04879719 and 0.02619028 Hartrees respectively, equivalently 30.62068kcalmol-1 and 16.43464kcamol-1.

Cis-butadiene
Ethylene

The HOMO and LUMO of each reactants are tabulated with their respective energies and symmetries (the orbitals are classified as symmetric and anti-symmetric with respect to the plane of symmetry shown);

Ethylene+Butadiene cycloaddition


Reactant Molecular Orbital Molecular Orbital Image Energy/Hartrees Energy/Hartrees (B3LYP/6-31G*) Symmetry w.r.t the plane
cis-butadiene HOMO

-0.34381 -215.74387 Anti-symmetric
LUMO

0.01707 10.71158 Symmetric
ethylene HOMO

-0.38775 -243.31661 Symmetric
LUMO

0.05283 33.15130 Anti-symmetric

Optmisation and Molecular Orbitals of the Transition Structure

Geometry of the guessed transition structure

The starting geometry of the transition state was obtained by orientating the optimised structure of ethylene so that it approached the optimised cis form of the butadiene from above. The distances between the terminal carbon atoms of each reactant were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise the transition structure.

The optimisation of the transition structure was successful which was confirmed by frequency analysis; an imaginary frequency at -956.65cm-1 representing two synchronous bond formations, which is expected for concerted Diels-Alder reaction. In contrast, the lowest positive frequency at 147.21cm-1 corresponds to the 'rocking' motion of ethylene, indicating that it not involved in the reaction pathway to a transiton state.

Vibration at -956.57cm-1 corresponding to the reaction path at the transition state
Vibration at 147.21cm-1 corresponding to the 'rocking' motion of ethylene

The optimised geometry of the transition struture is shown below, including the bond lengths of the partly formed σC-C bonds;

Comparison with typical sp3 and sp2 C-C bond lengths, 1.54Å1 and 1.34Å1, indicate that that the C=C bond lengths are in better agreement than the C-C bonds. The partly formed σC-C bond in the transition structure is 2.12Å, which is shorter than twice the van der Waals radius of a carbon atom, 1.71Å, but longer than a typical C-C bond. This suggests that the the van der Waals radii of the terminal carbon atoms are within each other to allow for bond formation, but because it is a transition structure, the bonds have not actually been formed yet.

The HOMO and LUMO are shown below with their respective energies;

Molecular Orbital Molecular Orbital Image Energy/Hartrees Energy/kcalmol-1 Symmetry w.r.t the plane
HOMO

-0.32396 -203.28782 Anti-symmetric
LUMO

0.02319 14.55193 Symmetric


By comparing the molecular orbitals of the transition structure with the those of reactants, it can be seen that the principal orbital interactions involve the π/π* orbitals of ethylene and the HOMO/LUMO of butadiene as expected. The LUMO of ethylene and HOMO of cis-butadiene are both anti-symmetric with respect to the reflection plane and overlap to form the HOMO of the transition structure, whilst the HOMO of the ethylene and LUMO of the butadiene overlap to form the LUMO of the transition structure because they are both symmetric. Thus, it is evident that orbital symmetry control is exhibited in such concerted reactions which is stated by Conservation of Orbital Symmetry3; transformation of the moelcular orbitals into the products proceed continuously by following the reaction path along which the symmetry of these orbitals remains the same as those of the reactants. Thus, reactions which follow the rule are classified as symmetry-allowed reactions; if the orbitals have different symmetry properties, then no overlap of electron density is possible and the reaction is forbidden.

Additionally, in terms of the molecular orbital energies, the energy difference between the HOMO of the cis-butadiene and LUMO of the ethylene is smaller to form the reactive HOMO (248.87kcalmol-1) than that of the orbitals which are involved in the LUMO of the transition structure(253.83kcalmol-1), thereby implying low kinetic stability.

References

  1. Fox, MA and JK Whitesell. Organische Chemie. 1994. Spektrum
  2. Bondi, A. (1964). "Van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–51. DOI:10.1021/j100785a001
  3. Hoffmann, R. Woodward, R.B. (1968). "Conservation of Orbital Symmetry" Acc. Chem. Res. 1 (1): 17–22 DOI:10.1021/ar50001a003

Cyclohexa-1,3-diene and Maleic Anhydride

Depending upon the orientation in which the dienophile i.e. the maleic anhydride appoaches the diene, two stereoisomer can be formed; the endo-isomer or the exo-isomer. In fact, cyclohexa-1,3-diene 1 undergoes a facile reaction with maleic anhydride 2 to give primarily the endo-adduct. The reaction is said to be kinetically controlled which suggests that the exo-transition state is higher in energy.

Diels-Alder reaction between cyclohexa-1, 3-diene and maleic anhydride1


Optimisation and Molecular Orbitals of the Transition Structure

Geometry of the initial guess transition structure
Geometry of guessed struture of endo-transition state

The initial guess of the transition state was obtained by orientating the optimised structure of maleic anhydride so that it approached the bicyclic system of the cyclohexa-1,3-diene from below to form the bridgehead (shown). The distances between the carbon atoms which form the σC-C bonds were appproximated to 2.0Å and then the frozen coordinate method was applied to characterise either the endo-/exo- transition structure.

Although, the rest of the molecule minimised successfully during freezing of the coordinates of the partly formed σbonds, the transition state optimisation failed; two negative force constants were calculated so Opt=NoEigen was inputted in the additional keywords to re-run the optimisation. However, this failed also, resulting in the transfer of hydrogens between the reactants suggesting that the reactants were located to close to each other. Thus, the intial guess structure was altered by increasing the distances between the carton atoms of the σC-C bonds to 2.4Å and symmetrizing the transition strcuture to Cs, and then as before the frozen coordinate method was applied.

Optimisation was successful and gave the exo-transition structure. In order to locate the endo-transition structure, the maleic anydride was flipped so that the hydrogens were pointing upwards as shown (shown). This time, the TS (Berny) optimisation was applied with the force constants calculated once, which successfully gave the endo-transition structure. Both structures are shown below with their respective energies and imaginary frequencies;

Exo TS Endo TS
Orientation of Hs2

Structure from side

Energy/Hartrees -0.05041981 -0.05150473
Energy/kcalmol-1 -31.63888 -32.31968
Imaginary frequency/cm-1 -812.17 -806.49


One can distungish between the geometries of the structures because in the exo-orientation, the substituents on the maleic anhydride, are pointing "up" away from the diene and the hydrogens are pointing "down". In theItalic text endo-orientation the substituents are pointing "down" towards the diene and the hydrogens are sticking "up".

Calculations show that the endo-transition structure exhibits a lower energy i.e it is more stable by 0.68kcalmol-1 than the exo-counterpart, which means the its activation energy is lower and thus confirms that it forms the kinetically controlled product, whilst the exo-transition structure corresponds to the product formed under thermodynamic control.

The various C-C bond lengths of the exo- and endo-transition structures were also compared as shown below;

Other C-C distances of exo-transiton structure
Other C-C distances of endo-transiton structure
C-C distances of σbond formations and C-C through space distnaces of exo-transiton structure
C-C distances of σbond formations and C-C through space distnaces of endo-transiton structure

The C-C bond lengths of both transition structures are very similar, including the lengths of the σC-C bond formations, 2.17Å in the exo- and 2.16Å in the endo-structures.

The C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo is 2.94Å and the “opposite” -CH=CH- for the endo is 2.89Å. The shorter distance in the endo supports the fact that secondary orbital interactions can occur, whereas this stereoelectronic effect is absent in the exo.

The exo-form could be more strained due to the steric repulsion experienced by the -CH2-CH2- fragment and the maleic anhydride ring. In the endo-form, the steric interactions are between the -CH=CH- fragment and the maleic anhydride ring, which is less due to the sp2 rather than sp3 hybvridsation of the carbon atoms.

The HOMO and LUMO of both transition structures are tabulated below with their respective energies and symmetries;

Molecular Orbital Molecular Orbital Image Energy/Hartrees (AM1) Energy/kcalmol-1 Symmetry w.r.t the plane
Exo TS HOMO

-0.34273 -215.06616 Anti-symmetric
LUMO

-0.04045 -25.38274 Anti-symmetric
Endo TS HOMO

-0.34505 -216.52198 Anti-symmetric
LUMO

-0.03571 -22.40835 Anti-symmetric


Both the HOMOs and LUMOs of each transition structure are anti-symmetric with respect to the plane of symmetry and it is the HOMO- LUMO overlap of the cyclohexa-1,3-diene and maleic anhydride respectively, which form the HOMO of the transition structures.

Both transition states exhibit primary HOMO-LUMO interactions leading to the formation of two σbonds. However, the preference for endo-stereochemistry is observed due to the overlap between the carbonyl group of the maleic anhydride and the developing pi bond at the back of the diene2. This interaction does not lead to the formation of new bonds but contributes to the stabilisation of endo-transition state with respect to that of the exo-one, suggesting that it is formed under kinetic control if the Diels-Alder reaction is irreversible. In contrast, the lack of this overlap in the exo-transition structure explains why this structure is higher in energy.

Secondary orbital overlap in the endo-transition structure

References

  1. Bearpark. M. (2009). "The Transition State" Imperial College London. http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3
  2. Clayden. J, Greeves. N, Warren. S and Wothers.P. (2001) Organic Chemistry. Oxford University Press: 916

Conclusion

Computational stimulations to characterise transition structures on potential energy surfaces allows to successfully determine the preferred mechanisms of the reactions. Furthermore, by studying the molecular orbitals of the transition structures we can apply the Conservation of Orbital Symmetry to determine which reactions are allowed/forbidden as well showing the secondary orbital intercations which are very important in determining the regioselectivity of Diels-Alder reactions.