Exploring the Fascinating World of Aromaticity: How Frontier and Perturbation Molecular Orbitals Approaches Help Us Understand the Enigmatic Hückel and Möbius Aromatic Compounds"

 

Exploring the Fascinating World of Aromaticity: How Frontier and Perturbation Molecular Orbitals Approaches Help Us Understand the Enigmatic Hückel and Möbius Aromatic Compounds"

Pericyclic reactions are a class of organic reactions that involve a cyclic reorganization of bonding and non-bonding electrons. These reactions are highly stereospecific and can be predicted and understood using molecular orbital theory. Frontier Molecular Orbital (FMO) and Perturbation Molecular Orbital (PMO) theory are two approaches used to explain pericyclic reactions.

Frontier Molecular Orbital (FMO) theory:

Frontier Molecular Orbital (FMO) theory is a widely accepted approach to explain pericyclic reactions. It states that the orbitals involved in a pericyclic reaction are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). The HOMO represents the electron-rich region of the molecule, while the LUMO represents the electron-poor region. The HOMO and LUMO are referred to as the frontier orbitals.

A methodology for quickly determining if a specific pericyclic reaction is allowed by looking at the symmetry of the lowest unoccupied molecular orbital (LUMO) in case of bimolecular reaction and the highest occupied molecular orbital (HOMO) (in the event of a unimolecular reaction).

Thus, electrocyclic reaction is analysed by HOMO of the open chain partner because reaction is uni-molecular reaction. The stereochemistry of an electrocyclic process is determined by the symmetry of the highest occupied molecular orbital (HOMO) of the open chain partner, regardless of which way the reaction actually runs. In thermal condition, HOMO is always ground state HOMO whereas in photochemical condition HOMO is always first excited state HOMO.

• If the highest occupied molecular orbital has m symmetry, the process will be disrotatory.
• If HOMO has C₂-symmetry then the process will be conrotatory.

The example including 4n+2 and 4n system is given below;

In a pericyclic reaction, the HOMO and LUMO orbitals interact to form a transition state, which is a high-energy intermediate state that occurs during the reaction. The HOMO-LUMO interaction can be either bonding or antibonding, depending on the nature of the reaction. The FMO theory explains the stereochemistry and regiochemistry of pericyclic reactions based on the interaction between the HOMO and LUMO orbitals.

Perturbation Molecular Orbital (PMO) theory:

Perturbation Molecular Orbital (PMO) theory is another approach used to explain pericyclic reactions. PMO was developed by H. Zimmerman and M. J. S. Dewar. It is based on the idea that the electronic structure of a molecule can be perturbed by an external field. The external field can be an electric field or a change in geometry caused by a reaction.

PMO theory involves the use of perturbation operators to modify the electronic structure of the molecule. The perturbation operators act on the molecular orbitals to create new orbitals that are used to describe the transition state of the reaction. The PMO theory is useful for predicting the reactivity of a molecule in a pericyclic reaction and can also be used to explain the stereochemistry and regiochemistry of the reaction.

PMO describes two aromatic systems;

• Hückel aromaticity
• Möbius aromaticity

As we know that aromaticity is a property of some organic molecules that have a cyclic arrangement of π-electrons with special stability and unique reactivity. Aromatic compounds are typically highly stable and exhibit unique reactivity, making them important in a wide range of fields including chemistry, biology, and materials science. 

Hückel Aromaticity:

Hückel aromaticity was first described by Erich Hückel in 1931. According to Hückel's rule, a molecule is considered aromatic if it meets the following criteria:

1. The molecule is cyclic.
2. The molecule is planar.
3. The molecule has a total number of π-electrons equal to 4n+2, where n is an integer.
4. System has no node then it is called Hückel system and array is called Hückel array.

A molecule that meets these criteria is considered to be Hückel aromatic. Some examples of Hückel aromatic compounds include benzene, pyridine, and furan.

The stability of Hückel aromatic compounds can be explained by the delocalization of π-electrons around the cyclic ring structure. The π-electrons are able to move freely around the ring, which stabilizes the molecule and makes it highly resistant to chemical reactions.

Möbius Aromaticity:

Möbius aromaticity is a less common type of aromaticity first proposed by Friedrich August Kekulé in the 19th century. A Möbius aromatic compound is defined as a cyclic compound that meets the following criteria:

1. The molecule is cyclic.
2. The molecule is non-planar.
3. The molecule has a total number of pi electrons equal to 4n, where n is an integer.
4. System has node then it is called Mobius system and array is called Mobius array.

A molecule that meets these criteria is considered to be Möbius aromatic. Some examples of Möbius aromatic compounds include cyclobutadiene and the cyclooctatetraene dianion.

The stability of Möbius aromatic compounds can be explained by the fact that the π-electrons are delocalized in a twisted, Möbius-like fashion around the cyclic ring structure. This delocalization leads to unique electronic and magnetic properties, making Möbius aromatic compounds useful in a variety of applications, including organic electronics and materials science. 

Transition state:

In transition state, thermal reactions take place via aromatic transition state [i.e., (4n + 2) π electrons having no node or (4n) π electrons having one node] whereas photochemical reactions proceed via antiaromatic transition state [i.e., (4n) π electrons having no node or (4n + 2) π electrons having one node].

For the thermal reactions involving (4n + 2) π electrons will be disrotatory and involved Hückel type transition whereas those having (4n) π electrons will be conrotatory and the orbital array will be of the Mobius type. Similarly, for photochemical reactions involving (4n + 2) π electrons will be conrotatory and involved Mobius type transition whereas those involving (4n) π electrons will be disrotatory and the orbital array will be Hückel type.

Conclusion:

Pericyclic reactions are important organic reactions that can be predicted and understood using molecular orbital theory. FMO and PMO theory are two approaches used to explain pericyclic reactions. FMO theory is based on the interaction between the HOMO and LUMO orbitals, while PMO theory is based on the perturbation of the electronic structure of the molecule. Both theories are widely used in the design and synthesis of new molecules and can be used to predict the stereochemistry and regiochemistry of pericyclic reactions. Hückel aromaticity and Möbius aromaticity are two important types of aromaticity that are based on the cyclic arrangement of π-electrons in organic compounds.