UPSC Combined Geo-Scientist, Mains · 2026 · Mains Paper III
Q8(b). π-MOs of butadiene; reactivity of dienes in the Diels–Alder reaction
Question
(i) Draw the π-molecular orbitals of 1,3-butadiene and arrange them in the order of their energy. Assign the HOMO and LUMO under thermal and photochemical conditions. (ii) Arrange the following dienes in the increasing order of reactivity towards maleic anhydride. Explain your answer: A 1,3-butadiene, B 2-tert-butyl-1,3-butadiene, C 2,3-di-tert-butyl-1,3-butadiene.
Answer in brief
(i) ψ₁<ψ₂<ψ₃<ψ₄ with 0, 1, 2, 3 nodes. Thermal: HOMO ψ₂, LUMO ψ₃. Photochemical: HOMO ψ₃, LUMO ψ₄. (ii) C < A < B.
Key points
- Four p orbitals give four MOs; each higher level has one more node: ψ₁ (0 nodes, all in phase, lowest), ψ₂ (1 node), ψ₃ (2 nodes), ψ₄ (3 nodes, all out of phase, highest). ψ₁,ψ₂ are bonding; ψ₃,ψ₄ antibonding.
- Four π electrons fill ψ₁ and ψ₂. Thermal (ground state): HOMO =ψ₂, LUMO =ψ₃. Photochemical: an electron is promoted ψ₂→ψ₃; the new HOMO is ψ₃ (singly occupied) and the LUMO is ψ₄.
- The Diels–Alder reaction needs the s-cis diene (the diene HOMO interacts with the dienophile LUMO); electron-donating alkyl groups raise the HOMO and speed up the reaction (normal electron-demand).
- the donor raises the HOMO; the bulky group at C-2 disfavours the s-trans conformer, so the s-cis population is higher: most reactive.
The full model answer
Worked out step by step, as it should go in the answer booklet. The solution sheet follows it.
(i) Molecular orbitals (5 marks)
- Four p orbitals give four MOs; each higher level has one more node: ψ₁ (0 nodes, all in phase, lowest), ψ₂ (1 node), ψ₃ (2 nodes), ψ₄ (3 nodes, all out of phase, highest). ψ₁,ψ₂ are bonding; ψ₃,ψ₄ antibonding.
- Four π electrons fill ψ₁ and ψ₂. Thermal (ground state): HOMO =ψ₂, LUMO =ψ₃. Photochemical: an electron is promoted ψ₂→ψ₃; the new HOMO is ψ₃ (singly occupied) and the LUMO is ψ₄.
(ii) Reactivity towards maleic anhydride (5 marks)
- The Diels–Alder reaction needs the s-cis diene (the diene HOMO interacts with the dienophile LUMO); electron-donating alkyl groups raise the HOMO and speed up the reaction (normal electron-demand).
- B (2-t-Bu): the donor raises the HOMO; the bulky group at C-2 disfavours the s-trans conformer, so the s-cis population is higher: most reactive.
- A: butadiene, reference reactivity (s-cis is about 2% in the equilibrium, but accessible).
- C (2,3-di-t-Bu): the two tert-butyl groups on the inner carbons clash with each other in the planar s-cis form, which is therefore forced out of planarity (twisted); the ends cannot reach the dienophile in a concerted suprafacial way: least reactive.
Order: C<A<B.
Coversfrontier orbitals, Diels–Alderπ-MOs of butadienereactivity of dienes in the Diels–Alder reaction
All parts of Question 8
- 8(a) Keto–enol tautomers of acetylacetone from ¹H-NMR10 marks
- 8(b) π-MOs of butadiene; reactivity of dienes in the Diels–Alder reaction10 marks
- 8(c) Claisen condensation from IR; structure of a monoterpene from ozonolysis10 marks