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 (HF) molecule, the hydrogen 1s atomic orbital and the fluorine half-filled 2pz atomic orbital overlap to form bonding and antibonding molecular orbitals, which are both \(\sigma\) (sigma) molecular orbitals. This overlap is symmetric around the bond axis, resulting in a strong covalent bond that stabilizes the hydrogen fluoride molecule.

Step-by-step solution

Understand orbital overlap

Orbital overlap is the process by which atomic orbitals of two atoms combine to form molecular orbitals in a new molecule. In the formation of a covalent bond, the atomic orbitals of the bonding atoms overlap, leading to the sharing of the electron pair between atoms. This results in a region of increased electron density between the atoms, creating a stable molecule.

Hydrogen 1s atomic orbital and Fluorine 2p atomic orbital

The hydrogen atom has only one electron, which occupies the lowest energy 1s atomic orbital. The fluorine atom has nine electrons, with two electrons occupying the 1s atomic orbital, two electrons occupying the 2s atomic orbital, and five electrons occupying the 2p atomic orbital. In the hydrogen fluoride molecule (HF), one electron from the hydrogen 1s orbital and one electron from the fluorine half-filled 2pz atomic orbital will combine to form a new molecular orbital.

Formation of bonding and antibonding molecular orbitals

When two atomic orbitals overlap, two new molecular orbitals are formed: a bonding molecular orbital and an antibonding molecular orbital. The bonding molecular orbital is formed when there's constructive interference between overlapping orbitals, resulting in a region of higher electron density and lower energy. Electrons in the bonding orbital stabilize the molecule. The antibonding molecular orbital is formed when there's destructive interference between overlapping orbitals, resulting in a region of lower electron density and higher energy. Electrons in the antibonding orbital destabilize the molecule.

Type of molecular orbitals formed in hydrogen fluoride

When hydrogen's 1s atomic orbital and fluorine's 2p atomic orbital overlap, a \(\sigma\) (sigma) type molecular orbital is formed. The reason for this is that a \(\sigma\) molecular orbital is symmetric around the bond axis, while a \(\pi\) (pi) molecular orbital is asymmetric with respect to the bond axis. In the hydrogen fluoride molecule, since the overlapping orbitals are symmetric around the bond axis, the resulting molecular orbitals will be \(\sigma\) molecular orbitals.

Conclusion

In the hydrogen fluoride (HF) molecule, the hydrogen 1s atomic orbital and the fluorine 2p atomic orbital overlap to form bonding and antibonding molecular orbitals, which are both \(\sigma\) (sigma) molecular orbitals. This overlap is symmetric around the bond axis, resulting in a strong covalent bond that stabilizes the hydrogen fluoride molecule.