Question

Which of the following molecules or ions are paramagnetic? What is the highest occupied molecular orbital (HOMO) in each one? Assume the molecular orbital diagram in Figure 9.18 applies to all of them. (a) NO (c) \(\mathrm{O}_{2}^{2-}\) (b) \(\mathrm{OF}^{-}\) (d) \(\mathrm{Ne}_{2}^{+}\) (e) CN

Short answer

Paramagnetic molecules/ions are NO and \(\mathrm{Ne}_{2}^{+}\). HOMOs are \(\pi^*\) for NO, \(\sigma^*\) for \(\mathrm{Ne}_{2}^{+}\), \(\sigma_2p^*\) for \(\mathrm{O}_2^{2-}\), \(\pi^*\) for \(\mathrm{OF}^-\), and \(\sigma_{2p}\) for CN.

Step-by-step solution

Understanding Paramagnetism

Paramagnetism occurs when there are unpaired electrons in a molecule or ion. Unpaired electrons contribute to a magnetic moment, attracting the molecule or ion to a magnetic field. To determine if a molecule or ion is paramagnetic, analyze its electron configuration to identify unpaired electrons.

Analyze NO for Paramagnetism

The molecule NO has 15 electrons. Its molecular orbital (MO) configuration is \(\sigma_{1s}^{2}\sigma^{*}_{1s}^{2}\sigma_{2s}^{2}\sigma^{*}_{2s}^{2}\sigma_{2p_{z}}^{2}\pi_{2p_{x},2p_{y}}^{4}\pi_{2p_{x},2p_{y}}^{*1}\). There is one unpaired electron in the \(\pi^{*}\) orbital, making NO paramagnetic. Its highest occupied molecular orbital (HOMO) is \(\pi_{2p_{x},2p_{y}}^{*1}\).

Analyze \(\mathrm{O}_{2}^{2-}\) for Paramagnetism

\(\mathrm{O}_{2}^{2-}\) has 18 electrons. Its MO configuration is \(\sigma_{1s}^{2}\sigma^{*}_{1s}^{2}\sigma_{2s}^{2}\sigma^{*}_{2s}^{2}\sigma_{2p_{z}}^{2}\pi_{2p_{x},2p_{y}}^{4}\pi^{*}_{2p_{x},2p_{y}}^{4}\sigma_{2p_{z}}^{*2}\). All electrons are paired, so \(\mathrm{O}_{2}^{2-}\) is not paramagnetic. Its HOMO is \(\sigma_{2p_{z}}^{*2}\).

Analyze \(\mathrm{OF}^{-}\) for Paramagnetism

This hypochlorite ion has 17 electrons. Its MO configuration is similar to that of NO but with an added electron: \(\sigma_{1s}^{2}\sigma^{*}_{1s}^{2}\sigma_{2s}^{2}\sigma^{*}_{2s}^{2}\sigma_{2p_{z}}^{2}\pi_{2p_{x},2p_{y}}^{4}\pi_{2p_{x},2p_{y}}^{*2}\). All electrons are paired, meaning \(\mathrm{OF}^{-}\) is not paramagnetic. The HOMO is \(\pi_{2p_{x},2p_{y}}^{*2}\).

Analyze \(\mathrm{Ne}_{2}^{+}\) for Paramagnetism

\(\mathrm{Ne}_{2}^{+}\) has 19 electrons. Its MO configuration is \(\sigma_{1s}^{2}\sigma^{*}_{1s}^{2}\sigma_{2s}^{2}\sigma^{*}_{2s}^{2}\sigma_{2p_{z}}^{2}\pi_{2p_{x},2p_{y}}^{4}\pi^{*}_{2p_{x},2p_{y}}^{4}\sigma_{2p_{z}}^{*1}\). There is one unpaired electron in the \(\sigma^{*}\) orbital, making \(\mathrm{Ne}_{2}^{+}\) paramagnetic. The HOMO is \(\sigma_{2p_{z}}^{*1}\).

Analyze CN for Paramagnetism

The molecule CN has 13 electrons. Its MO configuration is \(\sigma_{1s}^{2}\sigma^{*}_{1s}^{2}\sigma_{2s}^{2}\sigma^{*}_{2s}^{2}\sigma_{2p_{z}}^{2}\pi_{2p_{x},2p_{y}}^{4}\sigma_{2p_{z}}^{2}\). All electrons are paired, making CN not paramagnetic. Its HOMO is \(\sigma_{2p_{z}}^{2}\).

Key concepts

Molecular Orbital Theory

Molecular Orbital (MO) Theory helps us understand how atoms combine to form molecules. Instead of treating electrons as being localized between atoms, MO theory describes electrons as existing in molecular orbitals that extend over the entire molecule. These orbitals are created by the combination of atomic orbitals from the bonded atoms.
MOs are classified into bonding, anti-bonding, and non-bonding orbitals, each having different energy levels. Bonding orbitals stabilize the molecule as electrons occupy these lower-energy states, while anti-bonding orbitals can destabilize it if occupied.

• Bonding Orbitals: Lower in energy, they hold the atoms together.
• Anti-bonding Orbitals: Higher in energy, designated by an asterisk (*) symbol.

Understanding which orbitals are filled helps determine a molecule’s stability and its magnetic properties, as seen in whether they have unpaired electrons.

Electron Configuration

Electron configuration refers to the distribution of electrons in the molecular orbitals of a molecule. Each electron in a molecule occupies the lowest available energy orbital until all electrons are accommodated. The configuration can be represented using molecular orbital diagrams.
These diagrams show the specific order in which orbitals are filled, typically following Hund’s Rule and the Aufbau principle, which states that electrons occupy the lowest-energy available orbitals first.

• The notation, such as \(\sigma_{1s}^{2}\), represents electrons in different orbitals.
• Paired electrons have opposite spins and do not contribute to magnetism.

Analyzing the electron configuration is crucial in determining if a molecule is paramagnetic, as unpaired electrons indicate magnetic properties.

Chemical Bonding

Chemical bonding describes how atoms connect to form molecules through sharing or transferring electrons. In MO theory, bonding results from the overlap of atomic orbitals to form molecular orbitals. The extent and type of these overlaps dictate the strength and type of bond (covalent, ionic).
Covalent bonds, formed between atoms sharing electrons, are common in molecules analyzed using MO theory. The strength of these bonds can be predicted by understanding molecular orbital configurations.

• Stronger bonds result from filled bonding orbitals, while partial or filled anti-bonding orbitals can weaken bonds.
• Understanding bonding interactions helps explain a molecule's stability and reactivity.

The analysis of chemical bonding through MO theory provides insights into how molecules behave and interact.

Magnetic Properties

Magnetic properties of molecules are closely tied to their electron configuration. Paramagnetism occurs in molecules with one or more unpaired electrons, making them attracted to magnetic fields. In contrast, diamagnetic substances have all paired electrons and are slightly repelled by magnetic fields.
Checking for paramagnetism involves analyzing the molecule’s electron configuration to identify unpaired electrons. This is represented by either partially filled or singly occupied molecular orbitals.

• Paramagnetic: Presence of unpaired electrons. Examples include NO and \(\mathrm{Ne}_{2}^{+}\).
• Diamagnetic: All electrons are paired, as seen in \(\mathrm{O}_{2}^{2-}\) and CN.

Understanding a molecule’s magnetic properties aids in predicting its behavior in external magnetic fields and its potential applications in technology.