Question

Molecular Orbital Theory Sketch the bonding and antibonding molecular orbitals that result from linear combinations of the 2\(p_{z}\) atomic orbitals in a homonuclear diatomic molecule. (The 2\(\beta_{z}\) orbitals are those whose lobes are oriented perpendicular to the bonding axis.) How do these molecular orbitals differ from those obtained from linear combinations of the 2\(\beta_{y}\) atomic orbitals? (The 2\(p_{y}\) orbitals are also oriented perpendicular to the bonding axis, but also perpendicular to the 2\(\beta_{z}\) orbitals.)

Short answer

The bonding σ2pz molecular orbital has increased electron density between the atomic nuclei with no nodal planes, while the antibonding σ*2pz orbital has a nodal plane and reduced electron density between nuclei. These molecular orbitals differ from those formed by 2py orbitals, which create π (bonding) and π* (antibonding) orbitals with a side-to-side overlap, characterized by electron density above and below the bonding axis and a nodal plane on the axis for the antibonding orbital.

Step-by-step solution

Visualize the 2pz Atomic Orbitals

The 2pz atomic orbitals are oriented perpendicular to the bonding axis in a homonuclear diatomic molecule. The z-axis is typically chosen to be the internuclear axis. The 2pz orbitals have their lobes along this axis and consist of a positive and a negative lobe on each atom.

Combine the 2pz Orbitals to Form Molecular Orbitals

The bonding molecular orbital (σ2pz) is formed by the constructive interference (additive combination) of the 2pz orbitals. The lobes of the same sign from each atomic orbital overlap, leading to a region of increased electron density between the nuclei which constitutes a bonding interaction. The antibonding molecular orbital (σ*2pz), on the contrary, results from destructive interference (subtractive combination), where lobes of opposite signs overlap, creating a node between the nuclei where the electron density is significantly reduced, constituting an antibonding interaction.

Sketch the Molecular Orbitals

Draw both atomic 2pz orbitals overlapping constructively for the σ2pz molecular orbital, and overlapping destructively for the σ*2pz molecular orbital. The σ2pz has no nodal plane between the nuclei while the σ*2pz has one nodal plane.

Distinguish from 2py Orbitals

For 2py orbitals, since they are oriented perpendicular to both the bonding axis and the 2pz orbitals, their combination leads to pi (π) molecular orbitals rather than sigma (σ). The pi bonding orbital (π2py) is formed from side-to-side overlap and is located above and below the bonding axis, with no nodal planes between the nuclei. The pi antibonding orbital (π*2py) has a nodal plane on the bonding axis.

Key concepts

Understanding Homonuclear Diatomic Molecules

Homonuclear diatomic molecules consist of two identical atoms, like O₂ or N₂, bound together. They are simple yet fundamental in understanding chemical bonding from a molecular orbital perspective.

When two identical atomic orbitals from each atom combine, they form molecular orbitals—spatial regions where electrons can be found. These molecular orbitals are crucial because they accommodate the electron pairs that hold the atoms together.

In these molecules, the electrons fill molecular orbitals starting from the lowest energy level moving upwards, obeying the Pauli exclusion principle and Hund's rule, just like they do in atoms. The number of electrons from both atoms determines the filling of these orbitals according to molecular orbital diagrams, which are essential tools for predicting molecule stability and bond order.

Bonding and Antibonding Orbitals

Molecular orbitals come in two main types: bonding and antibonding.

• Bonding orbitals are lower in energy and result from the constructive interference of atomic orbitals. Electrons in these orbitals increase the electron density between the nuclei, which leads to a stable attraction and hence, a bond.
• Antibonding orbitals are the result of destructive interference of atomic orbitals. They are higher in energy and have a node between the nuclei. Electrons in these orbitals can destabilize a bond due to reduced electron density between the nuclei.

Both types are important in determining the overall stability and bond order of the molecule. For instance, if an antibonding orbital is filled, it can cancel out the bond created by a bonding orbital, which is a fundamental concept in predicting the behavior of molecules.

Sigma and Pi Molecular Orbitals

Sigma \(\sigma\) and pi \(\pi\) molecular orbitals form because of different types of overlap between atomic orbitals.

• Sigma orbitals (\sigma) occur when atomic orbitals overlap head-to-head. This direct overlap creates a cylindrical electron density area around the bond axis, which is often stronger than the \(\pi\) bond.
• Pi orbitals (\pi) result from side-to-side overlap of atomic orbitals. This overlap creates electron density above and below the bond axis. \(\pi\) bonds usually add to the strength of a \(\sigma\) bond in double and triple bonds.

The presence of \(\sigma\) and \(\pi\) bonds explains many properties of molecules, including bond strengths, lengths, and angles, crucial for understanding chemical reactions and molecular geometry.