Describe the bonding in \(\mathrm{NO}^{+}, \mathrm{NO}^{-}\), and NO using both the localized electron and molecular orbital models. Account for any discrepancies between the two models.

The localized electron model describes the bonding in a molecule in terms of localized electron pairs, which are localized between two adjacent atoms. This model mainly focuses on the valence electrons of the atoms and considers the formation of covalent bonds either by sharing a pair of electrons (single bond) or by sharing two pairs of electrons (double bond).

The molecular orbital model describes the bonding in a molecule in terms of molecular orbitals, which are formed by the linear combination of atomic orbitals. In this model, the electrons are not localized between two atoms, but are distributed throughout the molecule in molecular orbitals. The molecular orbitals can be bonding, anti-bonding, or non-bonding.

First, we will focus on the localized electron model and analyze the bonding in each molecule: 1. NO+: Nitrogen has 5 valence electrons and oxygen has 6 valence electrons. In NO+, there is a loss of 1 electron, and hence, the total valence electrons are 10. The nitrogen and oxygen atoms will form a double bond by sharing 4 of these electrons, with 3 electrons remaining as lone pairs on each atom. 2. NO-: In NO-, there is an additional electron, bringing the total number of valence electrons to 12. In this case, nitrogen and oxygen will form a double bond by sharing 4 of these electrons, with 4 electrons remaining as lone pairs on each atom. 3. NO: In NO, there are 11 valence electrons. The nitrogen and oxygen atoms will form a double bond by sharing 4 of these electrons. The remaining three electrons are distributed as unshared lone pairs: two on oxygen and one on nitrogen.

Now, we will focus on the molecular orbital model and analyze the bonding in each molecule: 1. NO+: The molecular orbitals formed by the combination of the atomic orbitals (2s and 2p) of nitrogen and oxygen in NO+ result in strong bonding between the two atoms. The electron configuration for NO+ is: \( \sigma_{1s}^{2} \sigma_{1s}^{*2} \sigma_{2s}^{2} \sigma_{2s}^{*2} \sigma_{2p}^{2} \pi_{2p}^{4} \pi_{2p}^{*2} \) 2. NO-: The molecular orbitals in NO- result in strong bonding between the nitrogen and oxygen atoms. The electron configuration for NO- is: \( \sigma_{1s}^{2} \sigma_{1s}^{*2} \sigma_{2s}^{2} \sigma_{2s}^{*2} \sigma_{2p}^{2} \pi_{2p}^{4} \pi_{2p}^{*3} \) 3. NO: In NO, the molecular orbitals are distributed such that the bonding between nitrogen and oxygen is relatively strong. The electron configuration for NO is: \( \sigma_{1s}^{2} \sigma_{1s}^{*2} \sigma_{2s}^{2} \sigma_{2s}^{*2} \sigma_{2p}^{2} \pi_{2p}^{4} \pi_{2p}^{*2} \)

The localized electron model and the molecular orbital model provide different perspectives for the bonding in NO+, NO-, and NO. The localized electron model is useful in providing a simple visual representation of electron sharing, while the molecular orbital model offers a more in-depth understanding of the electron distribution in these molecules. The main discrepancies between the two models arise from the fact that the localized electron model assumes electrons are localized between two atoms, while the molecular orbital model considers electrons to be delocalized throughout the molecule. This difference in focus can cause the bond strength predicted by the localized electron model to differ from the bond strength calculated using molecular orbitals. However, both models can still accurately describe the overall bonding trends in NO+, NO-, and NO.