Molecular Orbitals
MOLECULAR ORBITAL APPROACH
The approach of the dienophile (1) and diene (2) are shown below; notice the Highest Occupied Molecular Orbitals (HOMO1) to the bottom right of the diene which are for the butadiene portion of the diene that undergoes the bond formation with the Lowest Unoccupied Molecular Orbitals (LUMO) of the dienophile above. The LUMO of the dienophile are at the front of the picture. The correct 'polarity' of the molecular orbital coefficient is shown by the colours red or blue and these must be of the same colour to interect. The left hand side of the diene represents orbital overlap with the oxygen atoms in the six-membered ring and the C-O-C bond linking it to the diene. At the front of the diene the three methyl groups bonded to the silicon atom are clearly seen. On the quinol-based dienophile, the two hydrogen atoms protrude towards the viewer in front of the C=C group and the carbonyl group sticks out to the left and right. In fact, because the D-glucose auxiliary presents a more complicated molecular orbital picture due to the presence of the acetate groups (which don't interfere with the diene), these were removed in this model for simplicity.
Legend: Carbon atom: grey ball; hydrogen atom: turquoise; oxygen: red and silicon purple.
The energy level diagram is shown below and the smallest energy difference is clearly between the HOMO (2) and LUMO (1) (8.97 eV2)*:
Compare this to Danishefsky's Diene (3):
The energy level diagram is shown below and the smallest energy difference is clearly between the LUMO (1) and HOMO (3) (6.24 eV).
Interestingly, an article by A. K. Nacereddine et al.3 have found that the presence of a Lewis Acid catalyst changes a Diels-Alder reaction from an asynchronous concerted mechanism to a non-concerted one involving DFT4 study (B3LYP/6-31G*, GAUSSIAN 09). I wonder if the effects of Lewis Acid catalysts (described in the experimental), such as Eu(fod)3 would exert a similar mechanistic effect. Also, a fairly recent article from the Houk research group5 (using more advanced computational methods) has now found evidence for an organocatalytic Diels-Alder reaction previously thought (determined) to be concerted now to have a non-concerted (stepwise) mechanism!
*Update: using a semi-empirical (MNDO) single-point energy calculation (in vacuum) with Spartan 08, the HOMO of 2 and 3 and LUMO of 1 were estimated to be -6.15, -8.99 and -2.26 eV respectively (see ref. 6 and references within for this data); the corresponding the LUMO of 2 and 3 and HOMO of 1 were estimated to be -0.15, 0.36 and -6.32 eV respectively. The ELUMO - EHOMO of 1 and 2 = 3.89 eV. The global electrophilicity index, omega ω, for 1 and 2 were calculated to be 2.27 and 0.83 eV respectively (ref. 7 gives details about how to do the calculations). Nucleophilicity index, N, was found to be 0.16 eV. The electronic chemical potential, μ, was calculated to be -4.29 and -3.15 eV for 1 and 2 and chemical hardness, η, (ELUMO - EHOMO) was calculated to be 4.06 and 6.0 eV respectively. Semi-empirical methods have been used to calculate similar physical properties of other molecules8.
The molecular orbitals are better revealed below (compared to the Chem3D model above) for the dienophile 1 and TBDMS diene 2 (HOMO diene = -9.29 eV with PM3 method). The geometry optimised cis tri-isopropylsilyl analogue of 2 has a HOMO = -8.70 and LUMO 0.34 eV using the semi-empirical PM3 functional method with HyperChem 8.0 (see ref. 6 for its synthetic use); C1-O1-C1' = 116.93 degrees; C1-O1-C1'-O1' torsion angle = -86.98 degrees (similar to published data with the simpler s-trans TMS-ether9 in the crystal state)] using geometry restraints at these positions, but a skewered torsion angle (-34.73 degrees) in the C=C-C=C develops as seen (for an alternative planar reacting s-cis geometry the HOMO and LUMO are -8.76 and 0.19 eV).
It is easy to see the favoured topside attack of the dienophile (leading to an endo-transition state), with favoured (correct phase) orbital overlap. The HOMO density map reveals the asymmetry in its molecular orbitals (more orange/yellow colour = more HOMO density). Using hybrid DFT (B3LYP 6-31G**) with Spartan 14, the HOMO and LUMO of 1 (equilibrium/optimised geometry) was found to be -5.91 and -3.23 eV; for 2 (single-point) they are -6.26 and -1.33 (in vacuum) - a similar closer HOMO (diene): LUMO (dienophile) energy gap is seen (3.03 eV). See doi:10.7910/DVN/26971 for unpublished energy data (mostly DFT) with these and related molecules. The colours of the molecular orbitals are arbitrary and can be reversed throughout the molecule.
1. For a general article about FMO theory, see, K. Fukui, Role of Frontier Orbitals in Chemical Reactions, Science, 1982, 218, 747-754.
2. The energies of the MO's were calculated from Hückel surfaces using CambridgeSoft's Chem3D Pro software.
3. S. Bouacha, A. K. Nacereddine and A. Djerourou, A theoretical study of the mechanism, stereoselectivity and Lewis acid catalyst on the Diels-Alder cycloaddition between furan and activated alkenes, Tetrahedron Lett., 2013, 54, 4030-4033. DOI: 10.1016/j.tetlet.2013.05.079
4. W. Koch and M. C. Holthausen, A Chemist's Guide to Density Functional Theory, 2nd ed., Wiley-VCH, Weinheim, 2001.
5. A. Dieckmann, A. Breugst, and K. N. Houk, Zwitterions and unobserved intermediates in organocatalytic Diels-Alder reactions of linear and cross-conjugated trienamines, J. Am. Chem. Soc., 2013, 135, 3237-3242.
6. Miller, J.P. In Recent Advances in Asymmetric Diels-Alder Reactions in Advances in Chemistry Research; Taylor, J.C.; Ed.; vol. 18, Nova: New York, 2013, pp. 179-220. (ISBN: 9781622579112 publication or here).
7. A. M. Sarotti, Unraveling polar Diels–Alder reactions with conceptual DFT analysis and the distortion/interaction model, Org. Biomol. Chem., 2014, 12, 187-199.
8. R. Singh, D. Kumar, B. Singh, V. K. Singh, R. Sharma, Molecular structure, vibrational spectroscopic and HOMO, LUMO studies of S-2-picolyl-β-N-(2-acetylpyrrole) dithiocarbazate Schiff base by Quantum Chemical investigations, Res. J. Chem. Sci., 2013, 3, 79-84.
9. R.C. Gupta, D.S. Larsen, R.J. Stoodley, A.M.Z. Slawin, D.J. Williams, J. Chem. Soc., Perkin Trans. 1, 1989, 739-749.
Unpublished data, output and figures have been deposited at doi:10.7910/DVN/26971. Some of this data and further DFT updates, PhD thesis anthracycline chemistry/biochemistry and a computational study of the Diels-Alder reaction of naphthazarin and Danishefsky's diene is published here: doi:10.7910/DVN/ZAZ7Q1 and see ANTHRACYCLINE_PUBLICATION.PDF below.
Author: J. P. Miller. This article originally available from: “DIELS-ALDER FRONTIER MOLECULAR ORBITAL ORBITALS” Main Page, www.jonathanpmiller.com/orbitals/ [Accessed 08/05/2017].