Bio-organic and catalytic reaction mechanisms

Three families, one mechanism style. All pericyclic reactions are concerted — bonds break and form simultaneously around a cyclic array of overlapping orbitals, with no carbocation, radical, or other discrete intermediate along the way. They come in three types. Electrocyclic reactions interconvert an open conjugated polyene and a ring with one fewer $\pi$ bond and one new $\sigma$ bond (hexatriene $\rightleftharpoons$ cyclohexadiene). Cycloadditions join two separate $\pi$ systems into a ring using two new $\sigma$ bonds; the Diels–Alder reaction, a diene plus a dienophile giving cyclohexene, is the archetype and is classified as a $[4+2]$ cycloaddition. Sigmatropic rearrangements move a $\sigma$ bond across an adjacent $\pi$ system to a new position, labelled by how many atoms each end migrates over — a $[3,3]$-shift is the Cope/Claisen family.

The FMO shortcut. Instead of tracking every orbital in the molecule, pericyclic selectivity is predicted from just the frontier orbitals: the Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO). For a cycloaddition, the HOMO of one component must overlap constructively (in phase) with the LUMO of the other as the new $\sigma$ bonds form. For an electrocyclic reaction there is only one component, so it is the terminal-lobe phase pattern of that molecule's own HOMO that dictates how the chain must rotate to close the ring bond in phase.

Reading the electron count. The relevant quantity is the number of $\pi$ electrons taking part in the cyclic array, and only the parity of that number against $4n$ or $4n+2$ matters:

where: $N_\pi$ is the count of $\pi$ electrons in the pericyclic array (not the whole molecule), and $n$ is a positive integer that only fixes which of the two families $N_\pi$ falls into. Butadiene-type systems ($N_\pi = 4$) and hexatriene-type systems ($N_\pi = 6$) are the two cases that appear repeatedly at this level.

Conrotatory vs disrotatory. In an electrocyclic ring closure, the two open ends of the polyene must rotate so that lobes of matching phase meet. Disrotatory closure rotates the two ends in opposite senses (one clockwise, one anticlockwise); conrotatory closure rotates both ends the same way. Which one is allowed depends jointly on $N_\pi$ and on whether the reaction is thermal (ground-state HOMO) or photochemical (an electron is promoted, so the HOMO of the excited state is one orbital higher than the ground-state HOMO). For $N_\pi = 4n$, thermal is conrotatory and photochemical is disrotatory; for $N_\pi = 4n+2$, thermal is disrotatory and photochemical is conrotatory. That flip is the entire content of the Woodward–Hoffmann rules needed here — no symmetry-element derivation is expected, only fluent application.

Suprafacial vs antarafacial describes whether the two new bonds of a cycloaddition or sigmatropic shift form on the same face of a $\pi$ system (suprafacial) or on opposite faces (antarafacial). A thermal Diels–Alder $[4+2]$ is suprafacial on both components, which is why it proceeds readily on simple heating with no photochemical assistance.

Determine whether the thermal ring closure of (2E,4Z,6E)-octa-2,4,6-triene proceeds disrotatory or conrotatory, and predict the relative configuration of the new stereocentres.

Step 1. Count the $\pi$ electrons in the conjugated triene undergoing electrocyclisation: three double bonds contribute $N_\pi = 6$ electrons, so this is a $4n+2$ system with $n=1$.

Step 2. Apply the rule derived above: for $N_\pi = 4n+2$, the thermal electrocyclic reaction is disrotatory, because the ground-state HOMO ($\psi_3$ for a hexatriene-type system) has terminal lobes of matching phase.

Step 3. Translate rotation sense into stereochemistry: in a disrotatory closure the two terminal substituents rotate toward each other in a mirror-symmetric fashion. Given the (E,Z,E) geometry of the substrate, the terminal methyl groups end up cis on the newly formed ring, since disrotatory closure keeps substituents that started on the same face on the same face of the product ring.

Step 4. Contrast with photochemistry as a check: irradiating the identical substrate promotes an electron to what was the LUMO, inverting the requirement to conrotatory closure and delivering the trans diastereomer instead — the same substrate, opposite stereochemical outcome, confirming the thermal/photochemical flip from Step 4 of the derivation. Answer: thermal closure is disrotatory, giving the cis product; the photochemical pathway is conrotatory, giving the trans product.

Competitive stretch

Vitamin D biosynthesis runs the same logic inside the body. In skin, UV-B converts 7-dehydrocholesterol (a cyclohexadiene fused to the steroid skeleton) into previtamin D3 by ring-opening; the reverse of the octatriene closure above. What rotation sense operates, and what happens next? Since ring-opening is the microscopic reverse of the ring-closure just solved, the same $N_\pi = 4n+2$ ($n=1$) selection rule applies, but the process is now photochemical (driven by UV-B), so it proceeds conrotatory, fixing the specific triene geometry of previtamin D3. Previtamin D3 then undergoes a thermal $[1,7]$-sigmatropic hydrogen shift at body temperature over the following days, isomerising to the more stable vitamin D3 (cholecalciferol). The bio-organic point: the same conrotatory/disrotatory and sigmatropic-shift logic used for a bottle of octatriene on a lab bench also switches on vitamin D synthesis in living skin.

• Applying the $4n$ vs $4n+2$ rule to the wrong count — count only the $\pi$ electrons actually in the pericyclic array, not the total electrons in the molecule.
• Swapping conrotatory and disrotatory between thermal and photochemical conditions — excitation changes which orbital is frontier, which flips the rule for the same electron count.
• Treating pericyclic reactions as stepwise, with a discrete cation or radical intermediate — they are concerted, single-transition-state processes, which is exactly why their stereochemical outcome is so predictable.
• Assuming a Diels–Alder reaction needs no orbital-symmetry justification because it is "just addition" — its thermal, suprafacial-suprafacial allowedness is itself a direct consequence of HOMO(diene)-LUMO(dienophile) symmetry matching.

Ask the tutor: if the conrotatory/disrotatory flip between thermal and photochemical conditions is not clicking, or you want the HOMO node-count picture for a specific molecule drawn out, ask the AI tutor to walk through it visually.