Question

The commonly observed conversion of cyclopropy1 cations into allyl cations is considered to be an example of an electrocyclic reaction. (a) What is the HOMO of the ally1 cation? How many \(\pi\) electrons has it? (b) Would you expect conrotatory or disrotatory motion? (c) What prediction would you make about interconversion of allyl and cyclopropy1 anions? (d) About the interconversion of pentadienyl cations and cyclopentenyl cations?

Short answer

The allyl cation has 2 π electrons, and its HOMO is occupied by the π bond between the terminal carbon atoms. Conrotatory motion is expected due to the 4n (n=0) pattern of the π electrons. Interconversion of allyl and cyclopropyl anions is less likely under normal conditions due to differences in electron counts and molecular orbitals. Direct interconversion between pentadienyl and cyclopentenyl cations as a simple electrocyclic reaction is not expected due to the difference in their number of π electrons.

Step-by-step solution

a) HOMO of the allyl cation and its number of π electrons

The allyl cation has the molecular formula \(C_3H_5^+\) and its structure is that of an allyl group with a positive charge at the central carbon atom. In an allyl cation, the highest occupied molecular orbital (HOMO) is occupied by the π bond between the terminal carbon atoms. This HOMO has 2 π electrons.

b) Conrotatory or disrotatory motion

In electrocyclic reactions, whether conrotatory or disrotatory motion is observed depends on the number of π electrons involved. If there are 4n electrons involved in the reaction, conrotatory motion is expected, while for 4n+2 electrons, disrotatory motion is expected (where n is an integer). From part (a), we find that the allyl cation has 2 π electrons, which follows a 4n (n=0) pattern, indicating conrotatory motion is expected.

c) Interconversion prediction for allyl and cyclopropyl anions

An allyl anion is a negatively charged species with an unshared electron pair delocalized over three carbon atoms, and a cyclopropyl anion is a negatively charged species with electrons localized in a three-membered carbon ring. As per the Woodward-Hoffmann rules, which states that the π electron count determines the type of electrocyclic reaction, due to the difference in electron counts and molecular orbitals of both species, interconversion of these anions could be less likely under normal conditions.

d) Interconversion prediction for pentadienyl and cyclopentenyl cations

A pentadienyl cation has the molecular formula \(C_5H_7^+\) and consists of a five-carbon chain with two π bonds, and the cyclopentenyl cation has the molecular formula \(C_5H_7^+\) and consists of a five-membered ring with one π bond. There are 4 π electrons in a pentadienyl cation, and 2 π electrons in a cyclopentenyl cation. Since both cations have a different number of π electrons, we do not expect a direct interconversion between the pentadienyl and cyclopentenyl cations. It might be possible under specific conditions and with the presence of some catalyst or appropriate reagent, but not as a simple electrocyclic reaction.

Key concepts

HOMO and LUMO in organic chemistry

In organic chemistry, understanding the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO) is essential for analyzing how molecules behave and react. The HOMO is the orbital that contains the highest energy electrons that can participate in chemical reactions. On the other side, the LUMO is the lowest energy orbital that can accept electrons. These orbitals are crucial when predicting the ability of a molecule to act as a nucleophile (from HOMO) or an electrophile (from LUMO).
In the exercise above, the allyl cation's HOMO is the π bond between its terminal carbon atoms, consisting of 2 π electrons. Understanding which orbital is the HOMO helps predict how the molecule might interact with others, as the HOMO represents the active part in electron-sharing or transferring reactions. In the allyl cation, these π electrons can be used in reactions, playing a vital role in its reactivity.

π electrons

π electrons are those found in π bonds, typically formed by the side-to-side overlap of p orbitals. These electrons are particularly important in organic molecules because they are usually delocalized, contributing to the molecule's stability.
In the case of the allyl cation involved in the exercise, there are 2 π electrons within the HOMO. This small number qualifies under the electrocyclic reaction rule patterns that influence the rotational motion (conrotatory or disrotatory). The number of π electrons in a molecule dictates the type of motion and ordering in ring closure reactions, which is central to electrocyclic reactions. Understanding the behavior and distribution of π electrons is crucial in predicting reaction outcomes and stability of different molecular structures.

Woodward-Hoffmann rules

The Woodward-Hoffmann rules are guidelines used to predict stereochemical outcomes of pericyclic reactions, like electrocyclic reactions. These rules state that the stereochemistry of the product is determined by the number of π electrons participating in the transition.
For an electrocyclic reaction:

• If 4n π electrons are involved, conrotatory motion will occur, meaning the ends of the system rotate in the same direction.
• If 4n+2 π electrons are involved, disrotatory motion occurs, where ends rotate in opposite directions.

In the exercise, because the allyl cation involves 2 π electrons (an example of 4n, with n=0), a conrotatory motion would be anticipated during its interconversion reactions. Understanding these rules is pivotal in predicting how molecules will respond to changes in electronic or steric configurations, and ensure the accurate anticipation of products in synthetic organic chemistry.

Interconversion of cations and anions

The interconversion of cations and anions highlights how a molecule's ability to gain or lose electrons can result in a dramatic change in its structure and chemical properties. Cations are positively charged ions, whereas anions are negatively charged.
The differences in charge lead to distinct electron configurations, influencing the ability to convert between these two types of ions. In the exercise, converting between the allyl and cyclopropyl anions or between pentadienyl and cyclopentenyl cations involves significant changes in electron distribution.
The Woodward-Hoffmann rules help determine the likelihood of these interconversions. For example:

• Anion interconversion is less likely due to different electron localization in reactive species.
• Cation interconversion might need specific conditions, often involving catalysts, due to distinct electrons involved in their structures. These reactions are less straightforward and required careful consideration of conditions and molecular makeup.

Understanding these interconversions is crucial for designing synthetic pathways and predicting the stability and structure of reactive intermediates in organic reactions.