Question

Show how a hydrogen \(1 s\) atomic orbital and a fluorine \(2 p\) atomic orbital overlap to form bonding and antibonding molecular orbitals in the hydrogen fluoride molecule. Are these molecular orbitals \(\sigma\) or \(\pi\) molecular orbitals?

Short answer

In the hydrogen fluoride molecule, the hydrogen 1s atomic orbital overlaps linearly with the fluorine 2p_z atomic orbital, forming both bonding and antibonding σ molecular orbitals. The bonding σ orbital has electron density concentrated between the two nuclei, strengthening the bond, while the antibonding σ orbital has electron density outside the internuclear region, creating a repulsive force between the nuclei.

Step-by-step solution

Understand hydrogen and fluorine atomic orbitals

We need to understand the hydrogen 1s atomic orbital and fluorine 2p atomic orbital. In hydrogen, there is only one electron in the 1s atomic orbital, while in fluorine, there are six valence electrons, two each in the 2s and three in 2p orbitals. The 2p orbitals consist of three orbitals, 2p_x, 2p_y, and 2p_z, having lobes along the x, y, and z-axis respectively.

Describe the overlap process

In the hydrogen fluoride molecule, the hydrogen 1s atomic orbital overlaps end-to-end with one of the fluorine 2p atomic orbitals, specifically the 2p_z orbital, because the z-axis is typically chosen as the inter-nuclear axis. This linear overlap forms a molecular orbital, where the electron density is concentrated between the two nuclei, leading to a bonding interaction. In addition to the bonding molecular orbital, an antibonding molecular orbital is formed as well. In this orbital, the electron density is outside the internuclear region, leading to a repulsive force between the nuclei.

Identify the type of molecular orbitals formed

Molecular orbitals can be classified as σ (sigma) or π (pi) orbitals, depending on their symmetry around the molecular axis. When the overlap is along the molecular axis, such as in hydrogen fluoride, the orbitals formed are σ orbitals. In the case of hydrogen fluoride, both the bonding and the antibonding molecular orbitals are σ orbitals since the overlap occurs between 1s and 2p_z atomic orbitals.

Summarize your findings

In summary, the hydrogen 1s and fluorine 2p_z atomic orbitals overlap linearly in hydrogen fluoride to form both bonding and antibonding σ molecular orbitals. The bonding σ orbital has electron density concentrated between the two nuclei, making the bond stronger, while the antibonding σ orbital has electron density outside the internuclear region, leading to a repulsive force between the nuclei.

Key concepts

Bonding Orbital

A bonding molecular orbital is formed when atomic orbitals combine in such a way that there is an increase in electron density between the two nuclei. Think of it like glue that holds the atoms together.

• When two atomic orbitals overlap constructively, it means the wave functions are in phase. This results in a greater likelihood of finding electrons between the two nuclei.
• This increased electron density between the nuclei leads to a stabilizing effect because the electrons act as a cushion that counteracts the repulsive forces between the positively charged nuclei.

For the hydrogen fluoride molecule, the hydrogen 1s orbital and the fluorine 2p_z orbital overlap end-to-end along the inter-nuclear axis. This type of overlap forms a stable bonding orbital.

Antibonding Orbital

Antibonding molecular orbitals are the opposite of bonding orbitals. They form due to destructive interference of overlapping atomic orbitals.

• When atomic orbitals overlap out of phase, a nodal plane is created, where the electron density is essentially zero between the nuclei.
• Electrons in antibonding orbitals contribute to the instability of the molecule because they increase the energy and promote repulsion between the nuclei.

In the hydrogen fluoride example, while the bonding orbital pulls the atoms together, the antibonding orbital does the opposite. By having electron density largely outside the region between the two nuclei, it tends to push them apart.

Sigma Orbital

Sigma (\(\sigma\)) orbitals are the result of direct, head-on overlap between atomic orbitals.

• Sigma orbitals can be formed by the overlap of an s orbital and another s or p orbital.
• The key characteristic of a sigma orbital is rotational symmetry around the bond axis. The electron density is concentrated directly between the nuclei along the line joining them.

In the hydrogen fluoride example, the 1s orbital of hydrogen and the 2p_z orbital of fluorine overlap along the molecular axis to form both bonding and antibonding sigma orbitals. Here, both are classified as sigma because of the symmetry and direct overlap.

Pi Orbital

Pi (\(\pi\)) orbitals are a different type of molecular orbital resulting from the side-to-side overlap of atomic orbitals. Unlike sigma orbitals, pi orbitals do not have electron density directly along the axis joining the two nuclei.

• Typically, pi orbitals are formed from the side-by-side overlap of p orbitals, where electron density is found above and below the plane of the nuclei.
• Pi orbitals often come into play in scenarios where multiple bonds, such as double or triple bonds, are involved.

In the context of hydrogen fluoride, no pi orbitals are formed because the overlap involves end-to-end contact rather than a side-to-side arrangement. Instead, only sigma orbitals are relevant to this molecular arrangement.

Atomic Orbitals Overlap

The overlap of atomic orbitals is foundational for the formation of molecular orbitals. It's where individual atomic wave functions interact to create new molecular orbitals.

• There are constructive overlaps leading to bonding orbitals where the combined wave function results in increased electron density between nuclei.
• On the other hand, destructive overlaps lead to antibonding orbitals, where interference diminishes electron density between the nuclei.

In hydrogen fluoride, the optimal overlap between the hydrogen 1s and fluorine 2p_z orbitals determines the characteristics of the resultant sigma molecular orbitals. The specific alignment of these atomic orbitals is crucial for effective molecular bonding.