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Chapter 8: Problem 174

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

Expert verified
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

01

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.
02

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.
03

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.
04

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.

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Most popular questions from this chapter

Show the molecular orbital structure of \(\mathrm{H}_{2}\). Explain the molecular orbital structure both in terms of electron configuration and LCAO. Show the bonding orbital and antibonding orbital, and calculate the bond order.

The LCAO molecular orbital of the cyclopentadienate system \(\left(\mathrm{C}_{5} \mathrm{H}_{5}\right)\) have schematic energies as follows: Indicate a possible point of difference between \(\mathrm{C}_{5} \mathrm{H}_{5}^{+}\) and \(\mathrm{C}_{5} \mathrm{H}_{5}^{-}\) that can be deduced from molecular orbital theory

Discuss the various bonding and antibonding orbital of butadiene. Place them in order of increasing energy. What is the electronic configuration of butadiene in both the ground and the excited state.

Discuss the direct, concerted addition of \(\mathrm{H}_{2}\) to an alkene from the standpoint of orbital symmetry. (a) In the absence of catalyst, and (b) in the presence of photochemical stimulation.

(a) Define the following terms, and draw a diagram showing their relationship to each other. Amplitude Nodes Nodal plane Phase "Out of phase" Wave equation (b) How do they pertain to molecular orbitals?
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