Question

Sketch the bonding and antibonding molecular orbitals that result from linear combinations of the \(2 p_{x}\) atomic orbitals in a homonuclear diatomic molecule. (The \(2 p_{x}\) orbitals are those whose lobes are oriented along the bonding axis.)

Short answer

The bonding molecular orbital has overlapping lobes of the same phase between the nuclei without a node, while the antibonding molecular orbital has lobes of opposite phases leading to a node directly between the nuclei.

Step-by-step solution

Understanding Molecular Orbitals

Molecular orbitals are formed by the linear combination of atomic orbitals. When two similar atomic orbitals overlap along the bonding axis, bonding and antibonding molecular orbitals can form. Bonding orbitals have a lower energy and increase the electron density between the nuclei, stabilizing the molecule. Antibonding orbitals have higher energy and reduce electron density between the nuclei, which can destabilize the molecule.

Sketching the Bonding Molecular Orbital

To sketch the bonding molecular orbital for the combination of two 2px orbitals, draw both atomic orbitals with their phases (represented by different shadings or colors). The lobes of the same phase (same color or shading) should come together between the nuclei. This constructive overlap increases electron density between nuclei, and there should be no node (a plane where there is zero electron probability) between the nuclei.

Sketching the Antibonding Molecular Orbital

For the antibonding molecular orbital, again draw both 2px orbitals but this time with opposite phases (different shadings or colors) facing each other. The lobes of opposite phase come together and lead to destructive interference, creating a node (a plane with zero electron probability) directly between the two nuclei. This antibonding orbital has a region of zero electron density between the nuclei and has lobes pointing away from the nuclei.

Key concepts

Molecular Orbital Theory

Molecular Orbital Theory is a fundamental concept in chemistry that explains the electronic structure of molecules. Unlike atomic orbitals, which are associated with individual atoms, molecular orbitals belong to the entire molecule, offering a deeper understanding of chemical bonding.

When atoms come close to form a molecule, their atomic orbitals overlap to create new orbitals called molecular orbitals. These can hold the electrons of a molecule and are spread out over the entire molecule, influencing its stability, shape, and chemical properties. Molecular orbitals are described as combinations of atomic orbitals—mathematically, this is done through a process called linear combination of atomic orbitals (LCAO).

Molecular Orbital Theory helps to predict the distribution of electrons in a molecule, and consequently, its magnetic and bonding properties. According to this theory, electrons in molecules occupy molecular orbitals, starting with the lowest available energy states, similar to how they fill atomic orbitals in isolated atoms.

Bonding and Antibonding Orbitals

Understanding bonding and antibonding orbitals is crucial for comprehending molecular stability. Bonding orbitals are the result of constructive overlap of atomic orbitals. They are lower in energy and serve to draw two atoms together, increasing electron density between the atoms, thereby strengthening the bond and stabilizing the molecule.

In contrast, antibonding orbitals arise from destructive overlap of atomic orbitals, where the wave functions combine out of phase. These orbitals are higher in energy and push atoms apart, creating an area with low electron density between the nuclei, which generally makes the molecule less stable.

When sketching out these orbitals, bonding orbitals are depicted without any nodes between the nuclei, while antibonding orbitals have at least one node. The existence of nodes is directly tied to the phase relationship of the overlapping atomic orbitals.

Atomic Orbital Overlap

Atomic orbital overlap is the key to forming molecular orbitals. When two atomic orbitals come into proximity during molecule formation, they can overlap in two ways: end-to-end (sigma bonds) or side-by-side (pi bonds).

The end-to-end overlap is stronger and forms sigma bonds while the side-by-side overlap results in pi bonds. The 2px orbitals in homonuclear diatomic molecules generally form pi bonds since they are oriented parallel to each other along the bonding axis.

The extent and symmetry of the overlap help determine the bond order and strength. Proper orientation and phase matching between atomic orbitals are essential for effective overlap, and subsequently, a strong chemical bond.

Homonuclear Diatomic Molecules

Homonuclear diatomic molecules are composed of two atoms of the same element. The beauty of these molecules lies in the symmetry of their atomic orbitals, which simplifies the interaction between them when forming molecular orbitals.

For instance, in the linear combination of the 2px orbitals of a homonuclear diatomic molecule, the identical energy and shape of the atomic orbitals facilitate direct overlap along the internuclear axis. These overlapping orbitals can form both bonding and antibonding molecular orbitals, as observed in the process of sketching molecular orbitals for elements like nitrogen (N₂) or oxygen (O₂).

Understanding the energetics and symmetry involved in these molecules allows for the prediction of their bonding properties and how they might interact in chemical reactions. The molecular orbitals formed from the overlap of identical atomic orbitals in homonuclear diatomic molecules provide a clear illustration of how bonding and antibonding interactions dictate molecular stability.