Q4(c). Maleic anhydride: fast [4+2] with butadiene, no thermal [2+2] with ethene

Introduction. Both are cycloadditions of the C=C of maleic anhydride (the dienophile, electron-poor through two C=O groups). With butadiene it is a [4πₛ+2πₛ] (Diels–Alder) reaction, with ethene it would be a [2πₛ+2πₛ] reaction. Whether a concerted cycloaddition is allowed is decided by the frontier orbitals: the HOMO of one partner must overlap in phase with the LUMO of the other at both new bonds (Woodward–Hoffmann, Fukui).

Figure: Shaded lobes have one phase, open lobes the other. Arrow = bond forming; × = antibonding (out-of-phase) contact.

Butadiene + maleic anhydride: [4πₛ+2πₛ], allowed

1. The terminal lobes of the butadiene HOMO (ψ₂) have opposite signs at C-1 and C-4; the LUMO of maleic anhydride (π*) also has opposite signs at its two carbons. The patterns match: both new σ bonds can form with in-phase overlap, suprafacially on both components.
2. Equivalently, the six electrons move round a cyclic, aromatic (Hückel, 4n+2) transition state.
3. The -CO-O-CO⁻ group lowers the LUMO of the dienophile, so the HOMO–LUMO gap is small and the reaction is fast (it is complete in minutes at room temperature or on gentle warming in benzene).
4. Product: cis-1,2,3,6-tetrahydrophthalic anhydride (cyclohex-4-ene-cis-1,2-dicarboxylic anhydride); the cis geometry of maleic anhydride is kept (stereospecific syn addition).

Scheme: Concerted, suprafacial on both components; six-electron transition state.

Ethene + maleic anhydride: [2πₛ+2πₛ], forbidden

1. The HOMO of ethene (π) has the same phase at both carbons on one face; the LUMO of maleic anhydride (π*) has opposite phases at its two carbons. Face-to-face approach gives a bonding interaction at one end and an antibonding interaction at the other: no net bonding.
2. The four-electron cyclic transition state is antiaromatic (Hückel 4n): the concerted suprafacial–suprafacial path has a very high barrier.
3. The allowed [π2ₛ+π2ₐ] path needs one component to twist and bond through opposite faces, which is geometrically impossible for small alkenes; a stepwise path through a biradical would need energy far above that supplied under ordinary thermal conditions.
4. On irradiation the rule reverses: an electron in π* of the excited partner becomes the new HOMO, the phases match, and photochemical [2+2] cycloaddition of maleic anhydride to alkenes does occur (cyclobutane anhydrides).

Conclusion. With butadiene the [4πₛ+2πₛ] cycloaddition has in-phase HOMO–LUMO overlap at both termini (six-electron aromatic transition state): thermally allowed and fast, helped by the electron-poor dienophile. With ethene the [2πₛ+2πₛ] path has one bonding and one antibonding contact (four-electron, antiaromatic): thermally forbidden, so no reaction; it becomes allowed only photochemically.

Application. The maleic anhydride test for conjugated dienes (Diels–Alder adducts used to identify and estimate dienes in drying oils and terpenes) depends on this selectivity; photochemical [2+2] cycloadditions make cyclobutane rings, such as the thymine dimers formed in DNA by UV light.