Question

The \(2+2\) cycloaddition with one suprafacial and one antarafacial interaction is allowed. Show this conclusion via a frontier molecular orbital analysis. Although the reaction is allowed, it is seldom seen. Can you think of a reason not based on an orbital analysis of why this reaction is difficult?

Short answer

Based on the frontier molecular orbital analysis, a 2+2 cycloaddition reaction with one suprafacial and one antarafacial interaction is allowed, as the interacting orbitals have opposite symmetries and can undergo orbital overlap. However, this reaction is difficult because of steric hindrance, as an antarafacial interaction requires the reacting π systems to adopt a twisted or bent conformation, which is sterically unfavorable and increases the energy barrier.

Step-by-step solution

Understand the 2+2 cycloaddition reaction and the interaction types

A \(2+2\) cycloaddition reaction refers to the combination of two double bonds to form a cyclobutane moiety. Suprafacial and antarafacial interactions refer to the way electrons and orbitals interact during the reaction. In suprafacial interaction, the electron movements occur on the same face of the π system, while in antarafacial interaction, the electron movements occur on opposite faces of the π system.

Apply the Woodward-Hoffmann rules

The Woodward-Hoffmann rules help determine whether a reaction is allowed or not based on the orbital symmetries. For a reaction to be allowed, there must be a net retention of orbital phase during the formation of a new bond. So, we will apply these rules to the \(2+2\) cycloaddition reaction with one suprafacial and one antarafacial interaction.

Determine the symmetry of the involved orbitals

In a \(2+2\) cycloaddition reaction with one suprafacial and one antarafacial interaction, the orbitals involved are the Highest Occupied Molecular Orbitals (HOMO) of the two participating π systems. We need to determine the symmetry of the interacting orbitals: - For suprafacial interaction, the symmetry remains the same since electrons move on the same face. - For antarafacial interaction, the symmetry changes since electrons move on opposite faces.

Analyze the frontier molecular orbitals

We will now analyze the HOMO of the participating π systems in a \(2+2\) cycloaddition reaction with one suprafacial and one antarafacial interaction: - The HOMO of one π system undergoes a suprafacial interaction, and its symmetry remains the same (let's say it has the same symmetry as the parent molecule). - The HOMO of the other π system undergoes an antarafacial interaction, and its symmetry changes (opposite to the parent molecule). As the interacting orbitals have opposite symmetries, they can successfully undergo orbital overlap, and the reaction is allowed according to the Woodward-Hoffmann rules.

Provide a reason not based on orbital analysis for the difficulty of this reaction

Although the \(2+2\) cycloaddition reaction with one suprafacial and one antarafacial interaction is allowed based on the frontier molecular orbital analysis, it is rarely observed in practice. A reason not based on orbital analysis for this difficulty is the steric hindrance encountered during the reaction. In order for an antarafacial interaction to occur, one of the reacting π systems must adopt a twisted or bent conformation to allow the electron movement on opposite faces. This conformation is sterically unfavorable, leading to increased energy barriers and thus making the reaction difficult to occur.

Key concepts

Woodward-Hoffmann rules

Understanding the Woodward-Hoffmann rules is essential for chemists to predict the outcomes of pericyclic reactions. These rules originate from the study of orbital symmetry and are crucial for evaluating whether a reaction is 'allowed' or 'forbidden' under thermal conditions.

The rules state that pericyclic reactions can only occur if there is a conservation of orbital symmetry from reactants to products. In the context of a 2+2 cycloaddition, for the reaction to be symmetry-allowed, the orbital interactions must lead to the constructive overlap of electron orbitals. This involves considering whether the reaction proceeds through a suprafacial pathway, where electron movement occurs on the same side of interacting orbitals, or an antarafacial pathway, with electron movement on opposite sides.

In the given exercise, the 2+2 cycloaddition with one suprafacial and one antarafacial interaction conforms to the Woodward-Hoffmann rules because it maintains the necessary phase relationships for a constructive overlap of orbitals. It’s the symmetry and phase relation of the Highest Occupied Molecular Orbital (HOMO) that dictates the feasibility of such reactions according to these rules.

Frontier molecular orbital analysis

Frontier molecular orbital analysis is a pivotal tool in chemical reaction studies, particularly useful in understanding cycloaddition reactions like the 2+2 cycloaddition. This concept refers to the interaction between the HOMO of one reactant and the Lowest Unoccupied Molecular Orbital (LUMO) of the other.

For a successful reaction, there needs to be good overlapping between the HOMO of one molecule and the LUMO of another. The analysis focuses primarily on these 'frontier' orbitals because they are the highest and lowest energy orbitals that are capable of electron donation and acceptance, respectively. In the case of our exercise, both molecules contribute a HOMO since both are double bonds undergoing a cycloaddition.

By analyzing the symmetry properties of the frontier orbitals involved in the reaction – the suprafacial HOMO with unchanged symmetry and the antarafacial HOMO with changed symmetry – we deduce that the orbitals can overlap successfully. This orbital interaction is symmetry-allowed, which is why the reaction is theoretically viable according to the frontier molecular orbital theory.

Steric hindrance

Steric hindrance is a concept that also plays a significant role in the practical outcome of chemical reactions, such as the 2+2 cycloaddition. It explains why some reactions that are theoretically 'allowed' may still not occur readily in practice. Steric hindrance refers to the difficulty that atoms or groups of atoms face when approaching each other too closely in three-dimensional space.

In our specific exercise, even though the cycloaddition reaction is symmetry-allowed, the requisite antarafacial interaction implies that one of the π systems must bend or twist significantly to allow the correct orbital overlap. Such bending or twisting increases the spatial requirements of the reactants and can lead to significant repulsions between the electron clouds of approaching atoms or groups.

This strain introduces a high energy barrier that must be overcome for the reaction to proceed, making the 2+2 cycloaddition with antarafacial interaction sterically difficult and therefore less likely to occur under standard reaction conditions. Understanding steric effects is crucial for chemists to explain why certain reactions do not proceed despite being favorable from an orbital symmetry perspective.