30.9 A Summary of Rules for Pericyclic Reactions

Pericyclic Reaction Rules and Stereochemistry

Pericyclic reactions are concerted processes that proceed through cyclic transition states with no intermediates. Their stereochemical outcomes are entirely predictable if you know three things: the type of reaction, the number of electrons involved, and whether the reaction is thermal or photochemical. This section pulls together the selection rules for electrocyclic reactions, cycloadditions, and sigmatropic rearrangements into one unified framework.

Stereochemistry Prediction with TECA

The TECA mnemonic is a quick way to recall the selection rules for electrocyclic reactions and cycloadditions. Here's how it works:

• T = Thermal, E = Excited (photochemical, $h\nu$), C = Conrotatory, A = Antarafacial

The mnemonic encodes the "odd one out" pattern. For thermal reactions:

• 4n electrons → conrotatory (electrocyclic) / antarafacial (cycloaddition)
• 4n+2 electrons → disrotatory (electrocyclic) / suprafacial (cycloaddition)

For photochemical reactions, the rules flip:

• 4n electrons → disrotatory (electrocyclic) / suprafacial (cycloaddition)
• 4n+2 electrons → conrotatory (electrocyclic) / antarafacial (cycloaddition)

The practical takeaway: thermal [4+2] cycloadditions (like the Diels-Alder) are suprafacial-suprafacial and proceed readily, while thermal [2+2] cycloadditions are symmetry-forbidden because they would require an antarafacial component. Photochemical activation makes [2+2] cycloadditions symmetry-allowed through a suprafacial pathway.

Selection Rules for Pericyclic Reactions

The Woodward-Hoffmann rules, based on conservation of orbital symmetry, provide the theoretical foundation behind the TECA mnemonic. Frontier Molecular Orbital (FMO) theory offers an equivalent explanation: a pericyclic reaction is symmetry-allowed when the HOMO of one component and the LUMO of the other have matching symmetry for constructive overlap.

Electrocyclic Reactions

In a conrotatory closure, both terminal p orbitals rotate in the same direction, so substituents that were both "up" on the open-chain polyene end up on opposite faces of the ring (trans). In a disrotatory closure, they rotate in opposite directions, and substituents that were both "up" end up on the same face (cis).

Cycloadditions

Sigmatropic Rearrangements

Sigmatropic rearrangements involve migration of a $\sigma$ bond across a $\pi$ system. The selection rules follow the same electron-count logic:

• Thermal [1,5]-sigmatropic shifts (6 electrons, 4n+2): suprafacial migration, symmetry-allowed
• Thermal [1,3]-sigmatropic shifts (4 electrons, 4n): suprafacial migration with retention is symmetry-forbidden; the reaction requires antarafacial migration or inversion at the migrating center
• The Cope and Claisen rearrangements are [3,3]-sigmatropic shifts (6 electrons), thermally allowed through a chair-like suprafacial transition state

How Reaction Conditions Shape Outcomes

Thermal vs. photochemical activation is the single most important variable. Thermal reactions follow ground-state orbital symmetry; photochemical reactions promote an electron to the next MO, which reverses the symmetry of the HOMO and flips every selection rule.

Electron count determines which rule set applies. Count all the $\pi$ electrons (and any lone pairs) directly involved in the cyclic transition state. For electrocyclic reactions, count the $\pi$ electrons in the polyene. For cycloadditions, add the $\pi$ electrons from both components.

Substituent effects don't change the selection rules, but they strongly influence rates and regioselectivity:

• Electron-donating groups (EDGs like $-OCH_3$, $-NH_2$) raise the HOMO energy, making the molecule a better diene or nucleophilic partner
• Electron-withdrawing groups (EWGs like $-NO_2$, $-C=O$) lower the LUMO energy, making the molecule a better dienophile or electrophilic partner
• The best Diels-Alder reactions pair an electron-rich diene with an electron-poor dienophile, minimizing the HOMO-LUMO energy gap

Aromatic transition states are a unifying concept. Thermally allowed pericyclic reactions proceed through transition states with Hückel-type aromaticity (4n+2 electrons in a planar, suprafacial array), while photochemically allowed reactions proceed through Möbius-type aromatic transition states (4n electrons with one antarafacial component introducing a phase inversion). This is why the rules are so consistent across all three reaction types.