Question

How do the bonding and antibonding MOs formed from a given pair of AOs compare to each other with respect to (a) energy; (b) presence of nodes; (c) internuclear electron density?

Short answer

(a) Bonding MOs have lower energy; antibonding MOs have higher energy. (b) Bonding MOs have fewer nodes; antibonding MOs have more nodes. (c) Bonding MOs have higher internuclear electron density; antibonding MOs have lower density.

Step-by-step solution

Identify Molecular Orbitals (MOs)

Upon the combination of atomic orbitals (AOs), two types of molecular orbitals (MOs) are formed: bonding and antibonding. Bonding MOs are formed by the constructive interference of AOs, while antibonding MOs result from the destructive interference.

Compare Energy Levels

(a) Bonding MOs are lower in energy compared to the original AOs because they are more stable. In contrast, antibonding MOs are higher in energy because of their instability.

Nodes Presence Comparison

(b) Bonding MOs have fewer nodes compared to the antibonding MOs. Specifically, bonding MOs have no additional nodes apart from those present in the original AOs, while antibonding MOs have additional nodes.

Internuclear Electron Density

(c) Bonding MOs have higher electron density between the nuclei (internuclear region) which leads to a stronger bond. Antibonding MOs, conversely, have lower electron density in the internuclear region due to the presence of a node, resulting in a weaker bond.

Key concepts

Bonding Molecular Orbitals

When atoms come together to form molecules, their atomic orbitals (AOs) combine to form molecular orbitals (MOs). Some of these are bonding molecular orbitals. These MOs are formed when atomic orbitals interfere constructively. This constructive interference means that the atomic orbitals add up in such a way that the electron density between the nuclei increases. This increased electron density in the internuclear region stabilizes the molecule, pulling the nuclei together and lowering the energy of the system.
Bonding MOs are characterized by:

• Lower energy compared to the original atomic orbitals. This is because the increased internuclear electron density creates a more stable system.
• Fewer nodes. Nodes are points where the probability of finding an electron is zero. Bonding MOs generally have no additional nodes compared to the original atomic orbitals.
• Higher electron density between the nuclei, which strengthens the bond and stabilizes the molecule.

Understanding bonding MOs helps explain how molecules form and why certain bonds are stable.

Antibonding Molecular Orbitals

Not all molecular orbitals formed from the combination of atomic orbitals are stabilizing. When atomic orbitals interfere destructively, they form antibonding molecular orbitals. In these MOs, the electron density between the nuclei is reduced due to the presence of nodes.
Key features of antibonding MOs include:

• Higher energy than the original atomic orbitals. The presence of nodes, where electron density is zero, leads to decreased electrostatic attraction between the nuclei and the electrons, destabilizing the system.
• More nodes compared to bonding MOs. Antibonding MOs have at least one additional node, leading to regions where the probability of finding an electron is zero.
• Lower electron density in the internuclear region. This reduced electron density weakens the bond between the atoms and makes the molecule less stable.

Grasping the concept of antibonding MOs is crucial for understanding why some molecular structures are less stable and how bond formation and stability are influenced by the type of MOs formed.

Atomic Orbitals

Before we dive into the formation of molecular orbitals, it's essential to understand atomic orbitals (AOs). Atomic orbitals are the regions around an atom's nucleus where there is a high probability of finding an electron. Each orbital has a specific shape (like s, p, d) and energy level.

• Shapes: The shape of an atomic orbital influences how it can overlap with orbitals on other atoms to form molecular orbitals. For example, s orbitals are spherical, while p orbitals are dumbbell-shaped.
• Energy Levels: Electrons in atomic orbitals occupy the lowest available energy states, following the Aufbau principle. The energy level of atomic orbitals affects the energy of the resulting molecular orbitals.

When atoms come close to each other, their atomic orbitals interact to form molecular orbitals. This interaction can be constructive, leading to bonding MOs, or destructive, leading to antibonding MOs. The properties of the atomic orbitals, such as their energy and shape, play a crucial role in determining the characteristics of the molecular orbitals formed. Understanding AOs is fundamental to grasping the formation and properties of bonding and antibonding molecular orbitals.