A Comprehensive Guide: Frontier Molecular Orbital Approach and Perturbational Molecular Orbital Approach for Sigmatropic Rearrangements:

 

A Comprehensive Guide: Frontier Molecular Orbital Approach and Perturbational Molecular Orbital Approach for Sigmatropic Rearrangements:

Sigmatropic rearrangements are a class of organic reactions in which a sigma bond undergoes a shift, resulting in the formation of a new sigma bond and the breaking of an old one. These reactions are ubiquitous in organic chemistry and have been extensively studied over the years. Two approaches that have been employed to understand the mechanism of sigmatropic rearrangements are the Frontier Molecular Orbital (FMO) approach and the Perturbational Molecular Orbital (PMO) approach. In this article, we will provide a comprehensive guide on both these approaches and their applications in the context of sigmatropic rearrangements.

Frontier Molecular Orbital Approach:

The Frontier Molecular Orbital (FMO) approach is a theoretical method that utilizes the concept of frontier molecular orbitals to explain the reactivity of organic molecules. The FMO approach is based on the Hückel molecular orbital theory, which describes the electronic structure of π-conjugated systems. According to this theory, π-conjugated systems have a set of molecular orbitals that are energetically close to each other, known as the frontier molecular orbitals. These orbitals are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO).

In the FMO approach, the HOMO-LUMO energy gap is used to predict the reactivity of a molecule towards a particular reaction. For sigmatropic rearrangements, the FMO approach is used to determine the thermal and photochemical reactivity of the reactant molecules. The approach provides insights into the preferred direction of the reaction, the activation energy, and the stereochemical outcome of the rearrangement.

Here are some examples;

Mechanism

Here the noteable thing is 1,5 sigmatropic rearrangement occuring thermally is symmetrically allowed While 1,5 sigmatropic rearrangement occuring photochemically gives 1,3 product. 

[1, 3] Sigmatropic Rearrangement:

[1, 3] Sigmatropic Rearrangement is found in allylic compounds. The rearrangement is given below;

Mechanism

Keep in mind; Allylic HOMO is asymmetric and antarafacial in ground state while symmetric and Suprafacial in excited state.

[1, 5] Sigmatropic Rearrangement:

[1, 5] Sigmatropic Rearrangement is found in Pentadienyl compounds. The rearrangement is given below;

Selection rules for Sigmatropic Shifts:

Perturbational Molecular Orbital Approach:

The Perturbational Molecular Orbital (PMO) approach is another theoretical method used to study sigmatropic rearrangements. The PMO approach is based on the idea that the reaction proceeds through a transition state that is formed by the interaction between the reactant and the product molecules. The interaction between these molecules can be described by perturbing the electronic structure of the reactant molecule.

In the PMO approach, the reactant molecule is perturbed by a small amount, and the resulting electronic changes are used to calculate the interaction energy between the reactant and the product molecules. This interaction energy is then used to determine the activation energy and the transition state geometry of the rearrangement. The PMO approach is particularly useful for understanding the effects of substituents on the reactivity of the reactant molecule.

Here are some examples showing the PMO approach;

[1, 3] Sigmatropic Rearrangement:

[1, 5] Sigmatropic Rearrangement:

[1, 7] Sigmatropic Rearrangement:

Selection rules for Sigmatropic Shifts:

Applications of FMO and PMO Approaches in Sigmatropic Rearrangements

The FMO and PMO approaches have been extensively used to study sigmatropic rearrangements in various systems. One of the most well-known applications of these approaches is the Cope rearrangement. The Cope rearrangement is a sigmatropic rearrangement that involves the migration of a vinyl group from one carbon to another in a cyclohexadiene system. The FMO approach has been used to predict the preferred direction of the rearrangement, and the PMO approach has been used to determine the transition state geometry.

Another important application of the FMO and PMO approaches is in the study of the Diels-Alder reaction. The Diels-Alder reaction is a cycloaddition reaction that involves the formation of a new sigma bond between a diene and a dienophile. The FMO approach has been used to predict the regioselectivity and the stereochemistry of the reaction, while the PMO approach has been used to determine the effects of substituents on the reactivity of the reactant molecules.

Conclusion

In conclusion, the Frontier Molecular Orbital (FMO) approach and the Perturbational Molecular Orbital (PMO) approach are two powerful theoretical methods used to study the mechanism of sigmatropic rearrangements. Both approaches provide valuable insights into the reactivity, activation energy, and transition state geometry of these reactions. The FMO approach is particularly useful for predicting the thermal and photochemical reactivity of reactant molecules, while the PMO approach is useful for understanding the effects of substituents on the reactivity of reactants. These approaches have found wide applications in studying various sigmatropic rearrangements, including the Cope rearrangement and the Diels-Alder reaction. Overall, the FMO and PMO approaches are important tools for understanding the fundamental principles of organic chemistry and can aid in the design of new reactions and synthetic strategies.