Only B₂ and O₂ will show an increase in bond order when one electron is added to the molecule. This is because the addition of the electron will fill an antibonding orbital, which will decrease the number of antibonding electrons in the molecule and increase the bond order.
Molecular orbital theory describes the bonding in molecules as the result of the interaction of atomic orbitals. When two atoms come together to form a molecule, their atomic orbitals combine to form new molecular orbitals. These molecular orbitals can be bonding, antibonding, or non-bonding.
Bonding orbitals are lower in energy than the atomic orbitals that combined to form them, and they contain more electrons than antibonding or non-bonding orbitals. This means that bonding orbitals are more stable than antibonding or non-bonding orbitals.
When one electron is added to a molecule, it will occupy the lowest energy available molecular orbital. If there is an empty bonding orbital that is lower in energy than any of the antibonding or non-bonding orbitals, the electron will occupy that bonding orbital. This will increase the number of bonding electrons in the molecule, and therefore increase the bond order.
In the case of B₂, the addition of one electron will fill the σ<sub>2p</sub>* antibonding orbital. This will decrease the number of antibonding electrons in the molecule, and therefore increase the bond order.
In the case of O₂, the addition of one electron will fill the π<sub>2p</sub>* antibonding orbital. This will decrease the number of antibonding electrons in the molecule, and therefore increase the bond order.
The other molecules listed in the image will not show an increase in bond order when one electron is added to the molecule. For example, in the case of Li₂, the addition of one electron will fill a non-bonding orbital. This will not change the number of bonding or antibonding electrons in the molecule, and therefore will not change the bond order.
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