Question

Explain the difference between the \(\sigma\) and \(\pi\) MOs for homonuclear diatomic molecules. How are bonding and antibonding orbitals different? Why are there two \(\pi\) MOs and one \(\sigma\) MO? Why are the \(\pi\) MOs degenerate?

Short answer

In homonuclear diatomic molecules, σ orbitals form when atomic orbitals overlap along the internuclear axis, leading to greater electron density between the nuclei and cylindrical symmetry. π orbitals form when atomic orbitals overlap above and below, or in front and behind the internuclear axis, creating a nodal plane and concentrated electron density. Bonding orbitals arise from constructive interference of atomic orbitals and have lower energy, while antibonding orbitals arise from destructive interference and have higher energy. The two π MOs and one σ MO occur due to the combination of s- and p-orbitals in molecular orbital formation. Finally, π MOs are degenerate because they have the same energy level, resulting from their similar electron density distribution and electrostatic interactions.

Step-by-step solution

1. Difference between σ and π MOs for homonuclear diatomic molecules

: In homonuclear diatomic molecules, atomic orbitals from two identical atoms combine to form molecular orbitals. These molecular orbitals can be classified into two types: Sigma (σ) molecular orbitals and Pi (π) molecular orbitals. Sigma (σ) molecular orbitals form when atomic orbitals overlap along the internuclear axis, leading to a greater electron density between the two nuclei. Due to this overlapping along the internuclear axis, σ orbitals have cylindrical symmetry around the internuclear axis. Pi (π) molecular orbitals, on the other hand, form when atomic orbitals overlap above and below, or in front and behind the internuclear axis. In this case, the electron density is concentrated above and below (or in front and behind) the internuclear axis, leading to a nodal plane containing the internuclear axis.

2. Difference between bonding and antibonding orbitals

: When atomic orbitals combine to form molecular orbitals, two types of interactions can occur: Bonding and antibonding. Bonding orbitals result from the constructive interference of atomic orbitals, leading to an increased electron density between the nuclei. This increased electron density provides a stabilizing effect and, as a result, the energy of the bonding orbital is lower than the atomic orbitals from which it forms. Antibonding orbitals arise from the destructive interference of the atomic orbitals, leading to a decreased electron density between the nuclei with a nodal plane along the internuclear axis. This decreased electron density creates a destabilizing effect, and the energy of the antibonding orbital is higher than the atomic orbitals from which it forms.

3. Reason behind having two π MOs and one σ MO

: This phenomenon occurs due to the nature of atomic orbitals that are involved in the molecular orbital formation. When an s-orbital combines with a nearby p-orbital along the internuclear axis, a σ orbital is formed. However, when the s-orbital combines with the other two p-orbitals that are perpendicular to the internuclear axis, two π orbitals are formed. Since there are two p-orbitals perpendicular to the internuclear axis and only one along the internuclear axis, we end up with two π MOs and one σ MO.

4. Reason behind π MOs being degenerate

: Degenerate orbitals are orbitals that have the same energy level. In the case of π MOs, the two orbitals formed by the overlap of the two p-orbitals perpendicular to the internuclear axis are energetically equivalent. They have the same energy because their electron densities are distributed similarly around the internuclear axis, and as a result, they are affected equally by the electrostatic interactions between the electrons and the nuclei. This leads to π MOs being degenerate, meaning they have the same energy level.

Key concepts

Sigma Molecular Orbitals

In the realm of molecular orbitals, understanding sigma (σ) molecular orbitals is key to grasping chemical bonding. Sigma orbitals emerge when atomic orbitals engage directly along the internuclear axis—the line connecting two nuclei in a molecule. This happens typically when s-orbitals or p-orbitals align face-to-face.

Because of this direct overlap, σ molecular orbitals possess a characteristic cylindrical symmetry. Imagine a smooth cylinder running through the line between two atoms where electron density is concentrated. This high degree of electron density between the nuclei leads to very strong bonds because the shared electrons are held tightly in place by both nuclei.

As a result, sigma bonds are usually the strongest types of chemical bonds in a molecule, fundamentally stabilizing the molecule and holding the participating atoms together tightly.

Pi Molecular Orbitals

Pi (π) molecular orbitals arise in a different fashion than their sigma counterparts. Instead of overlapping directly along the internuclear axis, p-orbitals overlap side-by-side. This can also be considered as overlap above and below or in front and behind the axis connecting the two nuclei.

This type of overlap generates two distinct regions of electron density, leading to the unique structure of π orbitals. Electrons are located primarily in these lobes, away from the direct path between the nuclei. While this structure allows for important interactions, such as those in conjugated systems, it doesn't contribute as much stabilization as σ orbitals due to the less direct overlap.

What's interesting is that π orbitals often come in pairs. This pairing phenomenon is due to the fact that p-orbitals not involved in σ bonding can overlap in two different perpendicular planes, leading to two π molecular orbitals.

Bonding vs Antibonding Orbitals

The formation of molecular orbitals brings about two types: bonding and antibonding orbitals. Bonding orbitals form when atomic orbitals combine constructively. This constructive interference increases electron density between the two nuclei, stabilizing the system by making it energetically favorable.

In contrast, antibonding orbitals arise from destructive interference between atomic orbitals. This type of interference creates a node along the internuclear axis—a region with no electron density. As a result, antibonding orbitals have higher energy than the original atomic orbitals and destabilize the molecular structure by opposing bonding.

Therefore, in energy terms, bonding orbitals are lower than their corresponding antibonding orbitals, which makes them more stable. This dynamic plays a crucial role in molecular stability and chemical reactivity.

Degenerate Molecular Orbitals

Degenerate molecular orbitals refer to orbitals that, despite being distinct in location or orientation, have the same energy level. In the case of π molecular orbitals, the concept of degeneracy is vividly observed.

When p-orbitals form π orbitals, those orbitals that lie perpendicular to the internuclear axis overlap in such a way that they create two levels of equivalent energy. This is because the lobes of these orbitals distribute electron density similarly around the nuclei, resulting in identical energy levels.

It's vital in chemistry as degenerate orbitals can influence how electrons fill an atom or how molecules interact. The degeneracy of these π orbitals ensures unique bonding capabilities and is critical in electronic configurations influencing molecular behavior and chemical properties.