Bearing in mind that [OH]^- is isoelectronic with HF,...

Bearing in mind that $[\mathrm{OH}]^{-}$ is isoelectronic with HF, construct an approximate MO diagram to describe the bonding in $[\mathrm{OH}]^{-} .$ What is the bond order in $[\mathrm{OH}]^{-} ?$ Does the MO picture of the bonding differ from that obtained in the previous question using VB theory?

Key Concepts

Isoelectronic Species

Isoelectronic species are molecules or ions that have the same number of electrons and a similar electronic structure despite being composed of different atoms. This concept helps in predicting bonding patterns and orbital arrangements because species with the same electron count, like [OH]? and HF, can often be expected to display analogous bonding characteristics.

Molecular Orbital (MO) Theory

MO theory describes the bonding in molecules by combining atomic orbitals from all constituent atoms to form molecular orbitals that are spread over the entire molecule. Electrons are then filled into these molecular orbitals according to the Aufbau principle, Pauli exclusion principle, and Hund’s rule. In this framework, both bonding (lower energy) and antibonding (higher energy) orbitals are considered to understand the overall electronic structure of the molecule.

Bond Order

Bond order is a measure of the strength and stability of a bond, defined in MO theory as one-half the difference between the number of electrons in bonding orbitals and the number in antibonding orbitals. For species like [OH]?, which is isoelectronic with HF, the bond order is determined by filling the corresponding molecular orbitals and typically results in a single bond. This quantitative concept correlates with bond length and bond strength.

Comparison of MO and VB Theories

While MO theory describes electrons as delocalized over the entire molecule via molecular orbitals, valence bond (VB) theory represents bonds as localized overlaps between atomic orbitals. Despite these differing conceptual pictures, both methods can yield similar predictions for simple diatomic molecules. In the case of [OH]?, the MO approach provides a clear picture of the electron distribution between bonding and antibonding interactions, and when compared with VB theory, it shows that both approaches result in the same effective bond order albeit through different reasoning regarding electron localization.

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