Pericyclic Reactions

Pericyclic reactions are a class of concerted reactions in which bond breaking and bond formation occur simultaneously in a cyclic transition state. They are characterized by their stereospecificity and regioselectivity. These reactions do not involve any intermediate ionic or radical species, which simplifies their mechanistic analysis. The key to understanding pericyclic reactions lies in the concept of orbital symmetry, as explained by the Woodward-Hoffmann rules. These rules predict the feasibility of pericyclic reactions based on the symmetry of the molecular orbitals involved in the reacting system.

The term "pericyclic" itself suggests reactions that occur in a ring-like or cyclic manner. In the transition state, the atoms involved rearrange in a closed loop. This concerted nature means that all bond changes happen in a single step, making the reaction pathway highly ordered. The Woodward-Hoffmann rules, developed by Robert Burns Woodward and Roald Hoffmann, provide a powerful theoretical framework for predicting whether a pericyclic reaction will occur under thermal or photochemical conditions.

Orbital Symmetry and Woodward-Hoffmann Rules

The Woodward-Hoffmann rules are based on the principle of conservation of orbital symmetry. This principle states that for a reaction to occur efficiently, the symmetry of the molecular orbitals of the reactants must be the same as the symmetry of the molecular orbitals of the transition state. In simpler terms, the atomic orbitals that are involved in the bond-making and bond-breaking processes must align their phases correctly to form a stable cyclic transition state.

The rules categorize pericyclic reactions into three main types:

1. Electrocyclic Reactions: Involve the formation or breaking of a sigma bond within a conjugated pi system, leading to a change in the degree of conjugation.
2. Cycloaddition Reactions: Involve the joining of two or more unsaturated molecules to form a cyclic adduct, creating new sigma bonds.
3. Sigmatropic Rearrangements: Involve the migration of a sigma bond from one atom to an adjacent atom within a conjugated pi system, accompanied by a shift in the pi electrons.

For each of these reaction types, the Woodward-Hoffmann rules consider two factors:

1. The number of electrons involved in the cyclic transition state: This includes both pi electrons and electrons from any involved sigma bonds.
2. The conditions under which the reaction occurs: Whether it is thermally induced (ground state) or photochemically induced (excited state).

The general rules are:

• For thermal reactions: A pericyclic reaction is allowed if the number of electrons in the cyclic transition state is (4n + 2), where 'n' is an integer (0, 1, 2, ...). These are also known as 4n+2 rules.
• For photochemical reactions: A pericyclic reaction is allowed if the number of electrons in the cyclic transition state is 4n, where 'n' is an integer (1, 2, 3, ...). These are also known as 4n rules.

Reactions that are "allowed" under specific conditions are generally facile and occur with high stereospecificity. Reactions that are "forbidden" under thermal conditions typically have very high activation energies and do not occur unless subjected to photochemical conditions, or they proceed through a stepwise mechanism involving intermediates.

It's important to remember that these rules apply to the number of electrons participating in the cyclic transition state. This includes pi electrons and electrons from sigma bonds that are being broken or formed.

Electrocyclic Reactions

Electrocyclic reactions are a type of pericyclic reaction that involves the formation or breaking of a sigma bond between the terminal atoms of a conjugated pi system. This process leads to a change in the degree of conjugation, converting a cyclic compound into an acyclic one, or vice versa. These reactions are reversible and are governed by the Woodward-Hoffmann rules concerning orbital symmetry.

Conrotatory and Disrotatory Motion

The key to understanding the stereochemistry of electrocyclic reactions is the concept of conrotatory and disrotatory motion. When a sigma bond is formed or broken in a conjugated system, the two ends of the system must rotate.

• Conrotatory motion: Both terminal groups rotate in the same direction (either both clockwise or both counterclockwise). This type of motion leads to the formation of a substituted cyclic product with specific stereochemistry.
• Disrotatory motion: The two terminal groups rotate in opposite directions (one clockwise, the other counterclockwise). This type of motion also leads to specific stereochemistry.

The Woodward-Hoffmann rules dictate which type of motion is allowed under thermal or photochemical conditions.

Thermal Electrocyclic Reactions

Under thermal conditions, electrocyclic reactions involving (4n + 2) pi electrons are allowed. These reactions proceed via a disrotatory motion.

Example: 1,3-Butadiene to Cyclobutene (4 pi electrons) This is a classic example. A 1,3-butadiene molecule has 4 pi electrons. According to the Woodward-Hoffmann rules, a 4 pi electron system should undergo electrocyclization photochemically (4n rule, n=1) via conrotatory motion to form cyclobutene. Thermally, this reaction is forbidden via disrotatory motion. However, the reverse reaction, the thermal opening of cyclobutene to 1,3-butadiene, involves the breaking of a sigma bond and the formation of a 4 pi electron system. This reverse reaction is allowed thermally (4n rule, n=1) via disrotatory motion.

Example: 1,3,5-Hexatriene to 1,3-Cyclohexadiene (6 pi electrons) 1,3,5-Hexatriene has 6 pi electrons. According to the Woodward-Hoffmann rules, a 6 pi electron system should undergo electrocyclization thermally (4n + 2 rule, n=1) via disrotatory motion to form 1,3-cyclohexadiene. This is a well-established thermal reaction.

Summary for Thermal Electrocyclic Reactions:

• (4n + 2) pi electrons: Allowed, proceeds via disrotatory motion.
• 4n pi electrons: Forbidden, proceeds via conrotatory motion only under photochemical conditions.

Photochemical Electrocyclic Reactions

Under photochemical conditions, the molecule is promoted to an excited state, which alters the symmetry of the molecular orbitals. This reversal of symmetry dictates that reactions involving (4n) pi electrons are allowed, proceeding via conrotatory motion.

Example: 1,3-Butadiene to Cyclobutene (4 pi electrons) When 1,3-butadiene absorbs light, it is promoted to an excited state with altered orbital symmetry. The electrocyclization of 4 pi electron systems like butadiene is allowed photochemically via conrotatory motion to form cyclobutene. This is the primary way cyclobutenes are formed from conjugated dienes.

Example: 1,3-Cyclohexadiene to 1,3,5-Hexatriene (6 pi electrons) The photochemical opening of a 6 pi electron cyclic system (like cyclohexadiene) to an acyclic triene is forbidden. The thermal opening is allowed via disrotatory motion.

Summary for Photochemical Electrocyclic Reactions:

• 4n pi electrons: Allowed, proceeds via conrotatory motion.
• (4n + 2) pi electrons: Forbidden, proceeds via disrotatory motion only under thermal conditions.

The stereochemistry observed in the product is a direct consequence of the allowed mode of motion (conrotatory or disrotatory). For instance, if a substituted butadiene undergoes disrotatory cyclization, the relative stereochemistry of the substituents in the starting material is preserved in the cyclic product.

Cycloaddition Reactions

Cycloaddition reactions are a crucial class of pericyclic reactions where two or more unsaturated molecules combine to form a cyclic compound. In these reactions, new sigma bonds are formed, and pi bonds are consumed. The most common type is the [4+2] cycloaddition, known as the Diels-Alder reaction. Cycloadditions are also governed by the Woodward-Hoffmann rules.

The Diels-Alder Reaction ([4+2] Cycloaddition)

The Diels-Alder reaction is arguably the most important and widely studied cycloaddition reaction. It involves the reaction between a conjugated diene (a 4 pi electron system) and a dienophile (an electron-deficient alkene or alkyne, typically a 2 pi electron system). The reaction forms a six-membered ring, usually a cyclohexene derivative, with the formation of two new sigma bonds and the consumption of one pi bond from the diene and one pi bond from the dienophile.

Mechanism and Orbital Symmetry: The Diels-Alder reaction is a [4+2] cycloaddition because it involves a 4 pi electron system (the diene) and a 2 pi electron system (the dienophile). The total number of pi electrons involved in the cyclic transition state is 4 + 2 = 6.

According to the Woodward-Hoffmann rules, a 6 pi electron system undergoes a thermal cycloaddition reaction. Therefore, the Diels-Alder reaction is thermally allowed. It proceeds in a concerted manner through a cyclic transition state, maintaining the stereochemistry of both the diene and the dienophile.

Stereospecificity: The Diels-Alder reaction is highly stereospecific.

• Diene: If the diene has cis substituents, the resulting cyclohexene ring will have cis substituents. If it has trans substituents, the product will have trans substituents.
• Dienophile: Similarly, cis-dienophiles yield cis-substituted products, and trans-dienophiles yield trans-substituted products.

This stereochemical retention is a direct consequence of the concerted, cyclic transition state where the relative positions of the substituents are maintained.

Regioselectivity: When unsymmetrical dienes and dienophiles react, regioselectivity becomes important. The substituents on the diene and dienophile tend to arrange themselves in a way that maximizes the overlap between the terminal carbons of the diene and the double bond of the dienophile, leading to specific substitution patterns. Often, electron-donating groups on the diene and electron-withdrawing groups on the dienophile enhance reactivity.

Other Cycloaddition Reactions

While [4+2] is the most common, other cycloadditions exist:

• [2+2] Cycloaddition: This involves two molecules each contributing 2 pi electrons, for a total of 4 pi electrons. According to the Woodward-Hoffmann rules, a 4 pi electron system is thermally forbidden but photochemically allowed. Thermal [2+2] cycloadditions often proceed via stepwise mechanisms involving diradical intermediates, leading to loss of stereospecificity. Photochemical [2+2] cycloadditions are common, especially for alkenes, forming cyclobutane rings.
• [3+2] Cycloaddition: This involves a 3-atom component (e.g., a allyl system, or a 1,3-dipole like an azide or nitrone) and a 2-atom component (an alkene or alkyne). The total number of pi electrons is 5. These reactions are often thermally allowed but might not follow strict Woodward-Hoffmann rules as neatly as 4n or 4n+2 systems due to the nature of the 3-atom component (often involving a lone pair or a sigma bond). A classic example is the Huisgen 1,3-dipolar cycloaddition.
• [2+2+2] Cycloaddition: This involves three components, typically two alkenes and one alkyne, or three alkynes, often catalyzed by transition metals. These are not strictly pericyclic in the Woodward-Hoffmann sense but are important for forming six-membered rings.

Understanding the electron count and whether it's 4n or 4n+2 is key to predicting the thermal or photochemical feasibility of these reactions.

Sigmatropic Rearrangements

Sigmatropic rearrangements are a type of pericyclic reaction where a sigma bond migrates across a conjugated pi system. This migration involves the breaking of an existing sigma bond and the formation of a new sigma bond, accompanied by a redistribution of the pi electrons. The migrating group moves from one atom to an adjacent atom. These reactions are also concerted and stereospecific.

Sigmatropic rearrangements are classified by two numbers, [i+j], which represent the number of atoms in the pi system that the migrating group moves across, starting from one side of the sigma bond and ending on the other. The migrating group itself is considered to have one atom. So, a [1+5] sigmatropic rearrangement means the migrating group moves across 5 atoms of the pi system, with the sigma bond breaking and forming at positions 1 and 6 relative to the migrating group's starting point. The total number of atoms involved in the cyclic transition state is i + j.

The Woodward-Hoffmann rules apply to sigmatropic rearrangements based on the total number of electrons involved in the cyclic transition state. This includes the electrons of the migrating sigma bond and the pi electrons of the conjugated system.

Common Sigmatropic Rearrangements

1. [1,5]-Hydrogen Shift: This is a common rearrangement in conjugated systems. For example, in 1,3,5-hexatriene, a hydrogen atom can migrate from a terminal carbon to the other terminal carbon. This involves a [1+5] shift.

• The migrating group is H (1 atom).
• The pi system it moves across involves 5 atoms.
• Total atoms in the cyclic transition state = 1 + 5 = 6.
• Total electrons involved = 1 (from the H-C sigma bond) + 5 (from the 3 pi bonds) = 6 pi electrons.

Since it's a 6 pi electron system, this rearrangement is thermally allowed. It proceeds via a concerted mechanism.

2. [3,3]-Sigmatropic Rearrangement (Claisen and Cope Rearrangements): These are very important and widely observed rearrangements. They involve the migration of a sigma bond across a system where the migrating group moves from atom 3 on one side to atom 3 on the other side.

• Total atoms in the cyclic transition state = 3 + 3 = 6.
• Total electrons involved = 1 (from the migrating sigma bond) + 5 (from the pi bonds) = 6 pi electrons.

Since it's a 6 pi electron system, [3,3]-sigmatropic rearrangements are thermally allowed.

Claisen Rearrangement: This occurs in allyl vinyl ethers. The allyl group migrates to the vinyl group.
Cope Rearrangement: This is the hydrocarbon analog of the Claisen rearrangement, occurring in 1,5-dienes.

Stereochemistry of [3,3]-Sigmatropic Rearrangements: The stereochemistry of the product depends on the geometry of the starting material and the orientation of the cyclic transition state (e.g., chair-like transition state). For example, in the Claisen rearrangement of cis-allyl vinyl ethers, the product is formed with specific stereochemistry due to the preferred chair-like transition state.

3. [1,3]-Hydrogen Shift: This involves a hydrogen atom migrating across a pi system where the migration is over 3 atoms.

• Total atoms in the cyclic transition state = 1 + 3 = 4.
• Total electrons involved = 1 (from sigma bond) + 3 (from pi bonds) = 4 pi electrons.

A 4 pi electron system is thermally forbidden. Therefore, [1,3]-hydrogen shifts are generally not observed under thermal conditions. They are photochemically allowed.

4. [2,3]-Sigmatropic Rearrangements: These rearrangements involve systems with a specific arrangement of atoms and electrons, often seen in allylic sulfoxides, amines, or phosphines. They do not directly fit the simple 4n or 4n+2 electron counting rule based on pi electrons and a sigma bond. Instead, they often proceed through a concerted mechanism involving adjacent atoms and orbitals, leading to a rearrangement. These are often thermally allowed.

The application of Woodward-Hoffmann rules to sigmatropic rearrangements helps predict their feasibility and stereochemical outcomes, making them powerful tools in organic synthesis.