This simple Diels-Alder reaction illustrates the interacting frontier orbitals of the Diene (bottom) and the Dienophile (top). Note that the former has four p-electrons [C=C-C=C]and the latter two [C=C]. The sign (+ or -)(here the colour) of the coefficients is the same and these frontier orbitals can overlap with no impediment. Thus, in the Diels-Alder reaction the developing overlap is bonding at both sites where new bonds are being formed. As always, to form a bond a highest occupied molecular orbital (Π) interacts with a lowest unoccupied molecular orbital (Π*). There is no unfavourable antibonding here, where opposite poles interact!
The reaction of ethene and butadiene occurs at ca. 200 oC and 350 atm. pressure to form cyclohexene. The butadiene-ethene transition state (determined using a DFT calculation with Spartan 14 (B3LYP with 6-31G(d) basis set and standard parameters) is also shown below. For this TS, Mulliken Bond Orders are 0.362 between C3-C4 and C5-C6. Natural charges are -0.430, -0.463, -0.463 and -0.430 for C3, C4, C5 and C6 (Mulliken charges -0.337, -0.298, -0.298 and -0.337). C4 and C5 would represent the dienophile component. Cartesian coordinates linked here. The interatomic distance between the molecules (from the carbon atom nucleii) is 2.27 Angstroms. Activation energy was calculated to be 16.65 kcal/mol at 298 K. The activation energy was calculated from the difference between the energy of the TS and sum of the reactants (cis geometry of the diene in geometry optimised conformation) and conversion of a.u. to kcal/mol. Before the cycloaddition, however, the diene occupies the trans conformation (it's energy differs by 3.3 kcal/mol (HF 6-31G*, 298.15 K). This value is lower than other reported values, e.g. Houk and co-workers, P.N.A.S., 2012, 109, 12860-12865 provided a value of 23.4. Interestingly, the same authors using the M06-2X/6-31G(d) functional reported an energy of 18.8 kcal/mol. The HOMO and LUMO of the diene and dienophile were found to be -6.30, -0.60, -7.26 and +0.51 eV so the ELUMO diene and EHOMO dienophile are slightly closer in energy (6.66 eV) using DFT B3LYP 6-31G(d)(equilibrium geometry) and favourable orbital interactions. The electrophilicity index, omega ω, for ethene and butadiene were found to be 0.73 and 1.04 eV respectively (the same reported for ethene and very close for butadiene (1.05) in L. R. Domingo, M. J. Aurell, P. Peréz, R. Contreras, J. Phys. Chem. A, 2002, 106, 6871-6875). An ab initio Hartree-Fock 6-31 G(d) calculation (equilibrium geometry) gave similar results for the diene and dienophile (-9.36, +0.58, -10.19 and +5.00 eV; ELUMO diene - EHOMO dienophile = 10.77 eV). The Ab initio values for ethene in exact agreement with V.A. Soloshonok, D.J. Nelson, Beilstein J. Org. Chem., 2011, 7, 744-758. Some time ago, the corresponding values for the diene and dienophile were reported as -9.1, +1.0, -10.5 and +1.5 eV (presumed semi-empirical) in I. Fleming's book, Frontier Orbitals and Organic Chemical Reactions, 1976, p. 118). Molecular orbitals from the DFT study shown here; the (equilibrium) geometry optimised/energy minimised structures are seen and the C-C-C-C torsion angle is -34.1o. Compare these findings to other theoretical work.
Important updates: this article may be of interest, C.-X. Cui, Y.-J. Liu, A thorough understanding of the Diels-Alder reaction of 1,3-butadiene and ethylene, J. Phys. Org. Chem., 2014, 27, 652-660. Also, starting from the molecular mechanics MM+ geometry (butadiene is s-cis and planar without any minor skewer effect), single-point DFT B3LYP 6-31G* energies still show the LUMO of the diene and HOMO of the dienophile to be slightly closer in energy (6.41 eV) compared to the LUMO of the dienophile and HOMO of the diene (6.58 eV), similar to above. Using a larger basis set (6-311+G*) the difference becomes even less by only 0.044 eV, considering the two favourable MO overlap options; this reduces further to 0.005 eV starting from the RM1 geometry.
How to cite (Harvard style), e.g.: Miller, J. 2014. Diels-Alder reaction. [online] Available at: http://www.jonathanpmiller.com/HOMO-LUMO.htm [Accessed: 21 June 2014]. This unpublished data, output and figures have been deposited at doi:10.7910/DVN/26971.
Diels-Alder reaction animation.
In this demonstration, the favoured approach to afford the major diastereomer of the dienophile (tautomeric form in situo is on top of the diene as shown by the blue arrow; the minor diastoreomer results from attack below. Click on the green button to change speed: