Understanding Pericyclic Reactions in terms of Symmetry-allowed and Symmetry-forbidden and Molecular orbital theory

 

Understanding Pericyclic Reactions in terms of Symmetry-allowed and Symmetry-forbidden and Molecular orbital theory:

Pericyclic reactions are a class of organic reactions that involve a cyclic rearrangement of electrons within a conjugated system of atoms. These reactions are highly stereospecific and are governed by the principles of orbital symmetry and molecular orbital theory.

The following key points are raised in MOT;

§  Molecular orbital can be described by the linear combination of atomic orbitals (LCAO). In a π molecular orbital, each electron that previously occupied a p atomic orbital surrounding an individual carbon nucleus now surrounds the entire part of the molecule that is included in the interacting p orbitals.

§  A p orbital has opposing phases for its two lobes. A covalent bond is created when two in-phase atomic orbitals come into contact. A node forms between two nuclei when two out-of-phase atomic orbitals come into contact with one another.

§  The same principles that govern how electrons fill atomic orbitals—the aufbau principle, the Pauli exclusion principle, and Hund's rule—apply to how they fill molecular orbitals: Only two electrons can occupy a given molecular orbital, and an electron enters the accessible molecular orbital with the lowest energy.

Figure displays an explanation of ethene's molecular orbitals. (One phase of the two lobes of a p orbital is represented by a blue lobe, while the other phase is represented by a pink lobe).  Ethene has one π bond, which results in two p atomic orbitals and two π molecular orbitals. A bonding π molecular orbital is produced by the in phase interaction of the two p atomic orbitals and is denoted by Ψ₁ (Ψ is the Greek letter psi). The isolated p atomic orbitals have more energy than the bonded molecular orbital. Ethene's two p atomic orbitals are capable of out-of-phase interactions as well. An antibonding π* molecular orbital Ψ₂, which has a higher energy than the p atomic orbitals, is produced by the interaction of out-of-phase orbitals. The atomic orbitals interact additively to produce the bonding molecule orbital, whereas they interact subtractively to produce the antibonding molecular orbital. In other words, the interaction between in-phase and out-of-phase orbitals pulls atoms away whereas the interaction between in-phase and in-phase orbitals binds atoms together. The two electrons in ethene are located in the bonding molecular orbital because two electrons can occupy a molecular orbital because electrons live in the available molecular orbitals with the lowest energy. All molecules with a single carbon-carbon double bond are represented by this molecular orbital diagram.

Due to its two conjugated bonds, 1,3-butadiene contains four p atomic orbitals. There are four possible linear combinations for four atomic orbitals. There are thus four molecular orbitals: Ψ₁, Ψ₂, Ψ₃ and Ψ₄ and Oscillations are retained, as you can see: Four molecular orbitals are created when four atomic orbitals are combined. The other half are antibonding molecular orbitals (Ψ₃ and Ψ₄), and half are bonding molecular orbitals (Ψ₁ and Ψ₂). Two electrons are in Ψ₁ and two electrons are in Ψ₂ because the four electrons will live in the available molecular orbitals with the lowest energy. Keep in mind that despite having varying energies, all molecular orbitals are legitimate and can coexist. All compounds with two conjugated carbon-carbon double bonds are represented by this molecular orbital image.

For instance, Ψ₁ has three bonding interactions and zero nodes between the nuclei, Ψ₂ has two bonding interactions and one node between the nuclei, Ψ₃ has one bonding interaction and two nodes between the nuclei, and has zero bonding interactions and three nodes between the nuclei. In 1,3-butadiene, the highest occupied molecular orbital (HOMO) is Ψ₂ and the lowest unoccupied molecular orbital (LUMO) is Ψ₃. Light of the right wavelength will boost an electron from a molecule's ground-state HOMO to its LUMO if the molecule absorbs the light from Ψ₂ to Ψ₃. At that point, the molecule is stimulated. The HOMO is Ψ₃ and the LUMO is Ψ₄ in the excited state. In a photochemical reaction, the reactant is in an excited state as opposed to the ground state in a thermal reaction.

 You should be aware that a molecular orbital is bonding if there are more bonding interactions than there are nodes between the nuclei, and it is antibonding if there are less bonding contacts than there are nodes between the nuclei.

A molecular orbital description of 1,3,5-hexatriene is shown in figure given below;

The concept of symmetry is central to the understanding of pericyclic reactions, as it can determine whether a reaction is allowed or forbidden.

Symmetry-allowed reactions

In terms of molecular orbital, if two p-orbitals are in phase or both have same lobes they have symmetry allowed. Symmetry-allowed reactions involve a change in the symmetry of the molecular orbitals in the reactants as they undergo a cyclic rearrangement of electrons. This change in symmetry must be consistent with the symmetry of the cyclic transition state. When the symmetry of the molecular orbitals and the transition state are the same, the reaction is allowed.

For example, the Diels-Alder reaction involves the reaction of a diene and a dienophile to form a cyclic product. The reaction is allowed when the HOMO of the diene and the LUMO of the dienophile have the same symmetry as the cyclic transition state. This allows for a smooth flow of electrons through the system, leading to the formation of the cyclic product.

Symmetry-forbidden reactions:

In terms of molecular orbital, if two p-orbitals are out of phase or both have different lobes generating a nodal plane then, they have symmetry forbidden. Symmetry-forbidden reactions involve a change in the symmetry of the molecular orbitals that is not consistent with the symmetry of the cyclic transition state. These reactions are generally disallowed and do not occur under normal conditions.

For example, the electrocyclic ring closure of 1,3,5-hexatriene involves a change in the symmetry of the molecular orbitals that is not consistent with the symmetry of the transition state. This results in a symmetry-forbidden reaction that does not occur under normal conditions.

Methods for explaining pericyclic reactions:

There are several methods that can be used to explain the principles of orbital symmetry and the behavior of pericyclic reactions. These methods include:

Molecular orbital theory:

This theory describes the behavior of electrons in a molecule using a set of mathematical functions called molecular orbitals. Molecular orbital theory can be used to predict the outcome of pericyclic reactions by analyzing the symmetry and energy levels of the molecular orbitals involved.

Frontier orbital theory:

This theory focuses on the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of the reactants in a pericyclic reaction. Frontier orbital theory can be used to predict the regio- and stereoselectivity of a reaction by analyzing the overlap of the HOMO and LUMO orbitals.

Woodward-Hoffmann rules:

These rules provide a set of guidelines for predicting the stereochemistry of pericyclic reactions based on the symmetry of the reactants and the transition state.

Conclusion:

In conclusion, energy of the molecular orbital increases, the number of bonding interactions decreases and the number of nodes between the nuclei increases. Understanding the principles of symmetry-allowed and symmetry-forbidden reactions is crucial for understanding the behavior of pericyclic reactions. Molecular orbital theory, frontier orbital theory, and Woodward-Hoffmann rules are important tools for predicting the outcome of pericyclic reactions and designing new reactions with specific stereochemical outcomes. By utilizing these methods, chemists can unlock new possibilities for organic synthesis and materials science.