Question

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

Short answer

The localized electron model predicts triple bonds for all three molecular species: \(\mathrm{NO}^+\), \(\mathrm{NO}^-\), and \(\mathrm{NO}\). However, the molecular orbital model provides a more accurate description and predicts different bond orders: bond order of 1.5 for \(\mathrm{NO}^+\), 1 for \(\mathrm{NO}^-\), and 2 for \(\mathrm{NO}\). These discrepancies arise due to differences in the electron distribution among orbitals in each model. The MO model provides a more accurate picture of bonding as it accounts for variations in bond strength and bond length of the three species.

Step-by-step solution

Localized Electron Model - Valence Bond Theory

In the localized electron model, we describe bonding in terms of hybridization of atomic orbitals and the overlap of these orbitals to form sigma and pi bonds. 1. \(\mathrm{NO}^+\): In this cation, nitrogen (N) has 4 valence electrons, and oxygen (O) has 6 valence electrons. Since there is a positive charge, we lose one electron. Thus, there are 9 valence electrons in total. We can describe nitrogen as having sp-hybridization, forming one sigma bond with oxygen. This leaves three unpaired electrons in nitrogen's 2p orbitals, and two unpaired electrons in oxygen's 2p orbitals. The unpaired electrons in the 2p orbitals can form two pi bonds, leading to a triple bond between nitrogen and oxygen. 2. \(\mathrm{NO}^-\): In this anion, nitrogen has 4 valence electrons, oxygen has 6 valence electrons, and we add one due to the negative charge. There are 11 valence electrons in total. Nitrogen can be described as having sp-hybridization, forming one sigma bond with oxygen. There are three unpaired electrons in nitrogen's 2p orbitals and three in oxygen's 2p orbitals. The unpaired electrons in the 2p orbitals can form two pi bonds, leading to a triple bond. The remaining electrons form a lone pair on oxygen. 3. \(\mathrm{NO}\): Nitrogen has 4 valence electrons, and oxygen has 6 valence electrons. There are 10 valence electrons in total. Nitrogen has sp-hybridization, forming one sigma bond with oxygen. There are three unpaired electrons in nitrogen's 2p orbitals and two in oxygen's 2p orbitals. The unpaired electrons in the 2p orbitals can form two pi bonds, leading to a triple bond. In all three cases, the localized electron model predicts a triple bond between nitrogen and oxygen.

Molecular Orbital Model

In the molecular orbital model, we form molecular orbitals by combining atomic orbitals. The molecular orbitals are filled in the order of increasing energy, following the aufbau principle. First, we need to determine the molecular orbitals formed: - 1 \(2\sigma\) bonding orbital and 1 \(2\sigma^*\) antibonding orbital from the interaction of the 2s orbitals. - 1 \(2\sigma_g\) bonding orbital and 1 \(2\sigma_u^*\) antibonding orbital from the interaction of the 2p orbitals along the internuclear axis. - 4 bonding orbitals (\(2\pi_{x}\) and \(2\pi_{y}\)) and 4 antibonding orbitals (\(2\pi_{x}^*\) and \(2\pi_{y}^*\)) from the interaction of the 2p orbitals perpendicular to the internuclear axis. Next, we fill in the electrons: 1. \(\mathrm{NO}^+\): 9 valence electrons can be placed as follows: \[\sigma(2s)^2, \sigma^*(2s)^1, \sigma(2p)^2, \pi(2p_x)^2, \pi(2p_y)^2\] This leads to a bond order of \[\frac{1}{2}(6 - 3) = 1.5\] which indicates a bond between single and double bond character. 2. \(\mathrm{NO}^-\): 11 valence electrons result in: \[\sigma(2s)^2, \sigma^*(2s)^2, \sigma(2p)^2, \pi(2p_x)^2, \pi(2p_y)^2, \sigma^*(2p)^1\] The bond order is \[\frac{1}{2}(6 - 4) = 1\], which indicates a single bond character. 3. \(\mathrm{NO}\): With 10 valence electrons: \[\sigma(2s)^2, \sigma^*(2s)^2, \sigma(2p)^2, \pi(2p_x)^2, \pi(2p_y)^2\] This results in a bond order of \[\frac{1}{2}(6 - 2) = 2\], indicating a double bond character.

Comparing the Models

The localized electron model predicts triple bonds for all three molecular species. However, the molecular orbital model predicts different bond orders: 1.5 for \(\mathrm{NO}^+\), 1 for \(\mathrm{NO}^-\), and 2 for \(\mathrm{NO}\). The molecular orbital model provides a more accurate picture of the bonding, as it accounts for the differences in the bond strength and bond length of the three species. These discrepancies arise due to the difference in the ways electrons are distributed among orbitals in each model.

Key concepts

Localized Electron Model

The Localized Electron Model (LEM) helps us understand molecular bonding by focusing on individual atoms and their electron sharing. It relies on concepts such as hybridization and atomic orbital overlap to explain how atoms come together to form molecules.

In the LEM, we often discuss bonds in terms of sigma (σ) and pi (π) bonds. Sigma bonds occur when orbitals overlap directly between bonding atoms, while pi bonds form when orbitals overlap side-to-side. Let's see how this works with different nitric oxide (NO) species:

• For o(N^+): Nitrogen has an sp hybrid orbital that overlaps with an oxygen orbital to form a σ bond. There are also unpaired electrons from nitrogen's 2p orbitals, allowing the formation of two o bonds leading to a triple bond characterization.


• In the o(N^-): Similarly, sp hybridization allows for one σ bond, and the presence of unpaired p electrons forms o leading to a triple bond perception with lone pairs on more electronegative oxygen.


• With o: The unpaired electrons on nitrogen and oxygen form π bonds resulting in a perceived triple bond.

In all these cases, the LEM suggests a robust connection, highlighting its simplicity but sometimes overlooking subtleties shown by other models.

Molecular Orbital Theory

Molecular Orbital Theory (MOT) provides a more nuanced view of bonding, emphasizing the formation of molecular orbitals from the linear combinations of atomic orbitals. Here, electrons are not confined to a space between specific atoms but are allowed to experience the entire molecule. This broader perspective can explain the full range of molecular behavior more accurately than localized approaches.

In the MOT framework, the filling of electrons occurs in a specific order, thanks to the Aufbau principle, filling the lowest energy orbitals first. Let's break down what this means for NO species:

• For o(N^+): With 9 valence electrons, the MOT describes energy considerations allowing a bond order of 1.5, indicating a combination of single and partial double bond character.


• For o(N^-): Incorporating an extra electron resulting in 11 electrons, the MOT points to a bond order of 1, signifying a single bond due to additional antibonding involvement.


• : Here valence electrons create a bond order of 2, describing a more traditional double bond type across the molecule.

Through this, MOT accounts for more subtle differences between NO species by evaluating the interactions of electrons in various molecular orbitals.

Valence Bond Theory

Valence Bond Theory (VBT) adds another layer to our understanding of how atoms bond in molecules. This theory builds on the idea of hybridization referenced in the Localized Electron Model. It asserts that atoms share electrons via overlapping orbitals and can offer insights into the geometry and strength of bonds.

For the nitric oxide species:

• In o(N^+): VBT suggests sp-hybridization at nitrogen, forming one σ bond and allowing nitrogen and oxygen to share electrons along π bonds, reflecting a mix in bond characteristics as predicted by the bond order from other theories.


• In o(N^-): It places emphasis on the hybridization pattern resulting in a σ bond and π interactions, again aligning with the expected bond length implications.


• In : By detailing overlap and electron sharing, VBT describes the double bond found naturally in the structure.

While VBT primarily offers a localized understanding, by considering hybridization and geometry, it explains why bonds form the spatial patterns they do, complementing the broader scope of Molecular Orbital Theory.

Bonds in NO Species

The nitric oxide species o(N^+, N^-, ) exhibit intriguing bonding characteristics that vary across the model spectrum. While VBT and LEM show consistent triple bond descriptions, the Molecular Orbital Theory provides more nuanced insights:

Each model offers its lens to examine how electrons contribute to bonding feature unique evaluations:

• NO, MotKH, demonstrates the stabilization or destabilization across descriptively composite orbitals.
• embodies how electron presence affects the pattern when transitioning from positivity to negativity. behavior changes as represented in bond order calculations.
• This can adjust understanding from a stable triple bond to perhaps a more defensible or less tenable structure.

Complexities arise when considering observed versus predicted data — VBT and LEM offer simpler academic views, while MOT predicts variations in bond strength reflecting electric or magnetic properties of the species.