Question

Using the molecular orbital energy ordering for second-row homonuclear diatomic molecules in which the \(\pi_{2 p}\) orbitals lie at lower energy than the \(\sigma_{2 p}\), draw MO energy diagrams and predict the bond order in a molecule or ion with each number of total valence electrons. Will the molecule or ion be diamagnetic or paramagnetic?

Short answer

To predict bond order, draw the MO energy diagram in the correct order for a second-row homonuclear diatomic molecule, fill in the valence electrons, calculate the bond order, and check for unpaired electrons to determine if the molecule or ion is diamagnetic or paramagnetic.

Step-by-step solution

- Understand Molecular Orbital Theory for Second-Row Homonuclear Diatomic Molecules

In molecular orbital theory for second-row homonuclear diatomic molecules (like O2, F2), the ordering of energy levels is such that the \(\pi_{2p}\) orbitals lie at a lower energy level than the \(\sigma_{2p}\) orbitals. Hence, when drawing MO energy diagrams, one must first fill the \(\pi_{2p}\) orbitals before the \(\sigma_{2p}\) orbitals.

- Draw Energy Level Diagram

On the energy diagram, start by placing the molecular orbitals in order of increasing energy: \(\sigma_{2s}\), \(\sigma_{2s}^*\), \(\sigma_{2p}\), \(\pi_{2p}\), \(\pi_{2p}^*\), and then \(\sigma_{2p}^*\). Label each of these molecular orbitals and draw lines corresponding to them.

- Fill the Molecular Orbitals with Electrons

Fill the molecular orbitals with the appropriate number of electrons, always obeying the Pauli exclusion principle (no more than 2 electrons per orbital) and Hund's rule (maximize the number of unpaired electrons when electrons occupy degenerate orbitals).

- Calculate Bond Order

Determine the bond order using the formula: Bond Order = (number of electrons in bonding MOs - number of electrons in antibonding MOs) / 2. A higher bond order indicates a stronger, more stable bond.

- Predict Magnetic Behavior

Look at the number of unpaired electrons in the molecular orbital diagram. If there are unpaired electrons, the molecule will be paramagnetic. If there are no unpaired electrons, the molecule will be diamagnetic.

Key concepts

MO Energy Diagrams

To understand molecules' bonding characteristics, molecular orbital (MO) energy diagrams are indispensable. They depict energy levels of molecular orbitals formed from atomic orbitals in diatomic molecules. When constructing these diagrams for second-row homonuclear diatomic molecules, we refer to a specific energy hierarchy: the \(\pi_{2p}\) orbitals are lower in energy than the \(\sigma_{2p}\) orbitals. This is in contrast with first-row diatomic molecules, such as nitrogen (N₂), where the \(\sigma_{2p}\) orbital is lower.

In the designated order, starting from lowest to highest energy, orbitals are filled with electrons. As per Pauli’s exclusion principle, each orbital can host two electrons with opposite spins, and Hund's rule ensures that electrons fill degenerate orbitals singly and with parallel spins before being paired. This filling dictates the magnetic and bonding properties of the molecule.
Improving the Understanding of Drawing MO Diagrams:

• Label each step correctly, starting with the lowest energy orbitals, \(\sigma_{2s}\) and \(\sigma_{2s}^*\), moving through the crucial \(\pi_{2p}\), and ending with \(\sigma_{2p}^*\).
• Visually indicate electron pairing to reinforce the Pauli exclusion principle.
• Show degenerate orbitals (\(\pi_{2p}\) and \(\pi_{2p}^*\)) at the same energy level to emphasize their equivalence.

These diagrams are not merely theoretical constructs but guide prediction of molecular properties, such as bond strength and magnetic character.

Bond Order Calculation

Bond order provides an indication of the bond strength between two atoms in a molecule. Calculating it is simple yet powerful and can be done from the MO diagram. The bond order is the difference between the number of electrons in bonding and antibonding molecular orbitals, divided by two. Mathematically, we express this as: \(\text{Bond Order} = \frac{\text{number of electrons in bonding MOs} - \text{number of electrons in antibonding MOs}}{2}\).

A positive bond order means that the molecule is stable. The higher the bond order, the stronger and more stable the molecular bond is. For example, a bond order of one signifies a single bond, while a bond order of two indicates a double bond. Zero or negative bond order suggests the molecule or ion does not tend to form in nature.
Key Points for Clarifying Bond Order:

• Ensure that you fully count all electrons in bonding and antibonding orbitals before calculating.
• Understand that bond order is not always an integer—it can be a fraction, reflecting partial bond character in some molecular species.
• Use bond order calculations to compare bond strength and stability across different molecules or ions with the same types of atoms.

By calculating the bond order from the MO diagram, you have a powerful tool to predict the stability of a molecule and its existence.

Paramagnetism and Diamagnetism

Molecules demonstrate magnetic properties based on the behavior of their electrons in response to external magnetic fields. These properties are categorized into paramagnetism and diamagnetism. Paramagnetic substances have at least one unpaired electron and are attracted to magnetic fields. In contrast, diamagnetic substances have all their electrons paired and show repulsion in the presence of a magnetic field.

The MO energy diagram plays a pivotal role in determining the magnetic character of a molecule. By examining the diagram, you check for unpaired electrons in molecular orbitals. If unpaired electrons are present, the substance will behave as a paramagnet. Conversely, if electrons are all paired up, the substance is diamagnetic.
Enhancing Understanding of Magnetic Properties:

• Use MO diagrams to highlight unpaired electrons, which directly correlate with paramagnetic behavior.
• Reinforce that diamagnetism occurs only when all electrons are paired, with emphasis on electron spins cancelling out the magnetic effects.
• While paramagnetism is easier to detect using magnetic susceptibility measurements, diamagnetism is a universal property but often weaker and overshadowed by paramagnetic effects when unpaired electrons are present.

By relating the MO energy diagrams to the presence or absence of unpaired electrons, students can predict the magnetic properties of molecules, an essential aspect of chemical bonding.