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 and the fluorine 2p atomic orbital overlap along the internuclear axis, resulting in the formation of σ bonding and σ* antibonding molecular orbitals. This is because their overlap is symmetric with respect to the internuclear axis. The σ bonding molecular orbital has increased electron density between the hydrogen and fluorine nuclei, while the σ* antibonding molecular orbital has decreased electron density between the hydrogen and fluorine nuclei.

Step-by-step solution

Understand Atomic Orbitals and Molecular Orbitals

Atomic orbitals represent the regions in space where electrons are most likely to be found in atoms. Molecular orbitals represent the regions in space where electrons are most likely to be found in a molecule. When two atoms combine to form a molecule, their atomic orbitals overlap to create molecular orbitals.

Recognize Bonding and Antibonding Orbitals

When atomic orbitals overlap, two types of molecular orbitals are created: bonding and antibonding orbitals. Bonding molecular orbitals are created when the overlap of atomic orbitals results in an increase in electron density between the nuclei of the atoms involved. This increased electron density leads to a stronger attractive force between the nuclei, resulting in a stable bound state. Antibonding molecular orbitals are created when the overlap of atomic orbitals results in a decrease in electron density between the nuclei of the atoms involved. This decreased electron density leads to a weaker attractive force between the nuclei, resulting in an unstable, high-energy state.

Understand σ and π Molecular Orbitals

Molecular orbitals can be classified as either σ (sigma) or π (pi) based on their symmetry with respect to the internuclear axis - the line connecting the nuclei of the two atoms involved in the bond. σ molecular orbitals have symmetric electron distributions around the internuclear axis, and the orbital can freely rotate around the axis. In contrast, π molecular orbitals have asymmetric electron distributions around the internuclear axis, and the orbital cannot rotate around the axis without breaking the bond.

Overlap of Hydrogen 1s and Fluorine 2p Atomic Orbitals

In the hydrogen fluoride molecule, the hydrogen 1s atomic orbital and the fluorine 2p atomic orbital will overlap. Since the hydrogen 1s orbital is spherical and the fluorine 2p orbital is dumbbell-shaped, their overlap can be visualized along the internuclear axis. The resulting molecular orbitals will be symmetric with respect to this axis.

Determine the Type of Molecular Orbitals Formed

As the overlap of hydrogen 1s and fluorine 2p atomic orbitals is symmetric with respect to the internuclear axis, the resulting molecular orbitals are σ orbitals. When these orbitals combine, they form a σ bonding molecular orbital with increased electron density between the hydrogen and fluorine nuclei, and a σ* antibonding molecular orbital with decreased electron density between the hydrogen and fluorine nuclei. In conclusion, the hydrogen 1s and fluorine 2p atomic orbitals overlap to form σ bonding and σ* antibonding molecular orbitals in the hydrogen fluoride molecule.