Question

In future chapters, we will encounter carbanions-ions in which a carbon atom has three bonds and a lone pair of electrons and bears a negative charge. Draw another contributing structure for the allyl anion. Now using cartoon representations, draw the three orbitals that represent the delocalized \(\pi\) system (look at Figure \(1.26\) for a hint). Which of the three orbitals are populated with electrons?

Short answer

The π-system in the allyl anion can be represented using three molecular orbitals formed by the overlapping of the p-orbitals on the carbon atoms involved in the π system: the lowest energy orbital having all three p-orbitals in-phase, the middle energy orbital with the p-orbitals on the first and third carbon atoms out-of-phase with the middle one, and the highest energy orbital with the p-orbitals on the first and third carbon atoms in-phase with each other but out-of-phase with the middle one. The allyl anion has four π electrons, which populate the lowest and middle energy orbitals, while the highest energy orbital remains unpopulated.

Step-by-step solution

Draw the Allyl Anion and its Contributing Structures

To draw another contributing structure for the allyl anion, consider the two structures below: 1. One structure in which the negative charge is on the first carbon atom. \(\mathrm{[CH_2=CH-CH_2^-]} \) 2. Another structure in which the negative charge is on the third carbon atom. \(\mathrm{[CH_2^{-}-CH=CH_2]} \)

Represent the Delocalized π System using Cartoon Representations

Next, we need to draw the three orbitals that represent the delocalized π system. These orbitals are molecular orbitals formed by the overlapping of the p-orbitals on the carbon atoms involved in the π system. 1. Lowest Energy Orbital: This orbital consists of all three p-orbitals in-phase and overlapping side-by-side. 2. Middle Energy Orbital: This orbital consists of the p-orbitals on the first and third carbon atoms out-of-phase with the one on the middle carbon. 3. Highest Energy Orbital: This orbital consists of the p-orbitals on the first and third carbon atoms in-phase with each other, but out-of-phase with the one on the middle carbon.

Identify the Populated Orbitals

To determine which of these orbitals are populated with electrons, consider the electron configuration of the allyl anion. The allyl anion has a total of four π electrons, two from the π bond between the first and second carbon atoms, and the other two from the lone pair on the negatively charged carbon atom. The allyl anion will populate its orbitals in the order of increasing energy: 1. The lowest energy orbital will be filled first with two electrons. 2. The middle energy orbital will be filled next with the remaining two electrons. 3. The highest energy orbital will remain unpopulated. Therefore, the populated orbitals are the lowest and middle energy orbitals.

Key concepts

Understanding Carbanions

Carbanions are fascinating chemical species, particularly significant in organic reactions. They feature a carbon atom with three bonds and an additional lone pair of electrons, contributing to a negative charge. This unique arrangement turns carbon, usually electronegative, into an electron-rich center poised to engage in chemical reactions.

A straightforward illustration of a carbanion is the allyl anion, as explored in the exercise above. The allyl anion showcases how the carbon atom at either end of the molecule can bear the negative charge, giving rise to two contributing structures. The interplay of these structures within a molecule is an excellent example of resonance, which stabilizes the carbanion through electron delocalization.

Resonance has profound implications for the reactivity and stability of carbanions. The capacity of the negative charge to resonate between different carbon atoms in these species lessens the intensity of the negative charge at any one point. Thus, carbanions are not as reactive as they might first appear. Their role in organic reactions often hinges on this delicate balance between charge distribution and molecular stability.

Delocalized Pi System Phenomena

Within organic molecules like the allyl anion, the delocalized π (pi) system plays a crucial role. This system comprises pi electrons that are spread out over several adjacent atoms, rather than localized between a single pair of atoms. Delocalization occurs through the overlapping of p-orbitals, allowing the electrons to move more freely across the molecule.

The presence of a delocalized π system bestows the molecule with enhanced stability through the phenomenon of resonance. As seen in the provided exercise, this system is represented by molecular orbital diagrams that visualize electrons' probable locations. In the allyl anion's case, three such orbitals depict the delocalized π system, ranging from the lowest energy level to the highest. Electrons will fill these orbitals starting from the lowest energy, leading to a distribution that affects chemical properties and reactivity.

The delocalization also has practical implications for the allyl anion's chemical behavior, particularly in reactions such as nucleophilic substitutions or polymerization processes. It is essential to understand this property when predicting the outcome of organic reactions involving such species.

Molecular Orbitals and Bonding

Molecular orbitals are central to understanding chemical bonding and electron distribution in molecules like the allyl anion. They are formed when atomic orbitals, the regions in an atom where there's a high probability of finding an electron, combine as atoms bind together to form a molecule.

These orbitals are classified based on their energy levels; electrons populate the orbitals beginning with the lowest energy. The exercise demonstrates that the allyl anion has a total of four π electrons, which occupy the molecular orbitals according to the Aufbau principle, filling up from the orbital with the lowest energy to higher ones.

Types of Molecular Orbitals

Each molecular orbital in the delocalized π system has a distinct shape and energy level:

• The lowest energy orbital is in-phase and consists of side-by-side overlap of p-orbitals.
• The middle energy orbital has the central p-orbital out-of-phase with the outer p-orbitals.
• The highest energy orbital is also out-of-phase but with a different phase alignment than the middle orbital.

Understanding the structure and filling of these orbitals is vital for grasping how electrons contribute to molecule stability and reactivity.

Electron Configuration in Anions

Electron configuration describes how electrons are distributed within molecular orbitals of an atom or a molecule. For the allyl anion, this configuration reflects the arrangement of its four π electrons among the available molecular orbitals.

Understanding the electron configuration of the allyl anion is a stepping stone to predicting its chemical behavior. The two electrons from the π bond and the two from the lone pair contribute to its electron configuration. As per Hund's rule, these electrons will occupy the available molecular orbitals in a way that minimizes repulsion, starting with the lowest energy orbital.

The electron configuration also impacts reactivity. The filled orbitals define the electron density distribution in the molecule and, hence, where it is most likely to engage in chemical reactions. By filling the lowest and middle energy orbitals, the allyl anion achieves a level of stability that influences how it interacts with other reactants. Understanding these distributions helps chemists to manipulate such species in various organic synthesis processes.