Final answer:
Molecular Orbital Theory uses bonding and antibonding orbitals to determine the stability of molecules and ions, with the bond order indicating stability. A bond order greater than zero suggests stability, while zero or negative bond orders indicate instability, such as with the H₂²- ion.
Step-by-step explanation:
Using Molecular Orbital Theory to Predict Stability
Molecular Orbital (MO) Theory is a sophisticated method for describing the distribution of electrons in molecules. It uses atomic wave functions to construct molecular orbitals that can be bonding or antibonding. Bonding molecular orbitals stabilize a molecule by distributing electron density between the nuclei, while antibonding molecular orbitals are destabilizing as they distribute electron density away from the internuclear region. Whether a molecule or ion is stable can be ascertained by its bond order, which is calculated as the difference between the number of electrons in bonding and antibonding molecular orbitals, divided by two.
To predict the stability of a molecule or ion such as the H₂²- ion or C₂²-, one must draw its molecular orbital energy-level diagram, populate it with the corresponding number of valence electrons, and calculate its bond order. A positive bond order typically indicates a stable molecule or ion, while a bond order of zero or negative suggests instability. In the case of the H₂²- ion, the addition of two extra electrons to antibonding orbitals leads to a bond order of zero, indicating instability.