Question

Construct a molecular orbital diagram for \(\mathrm{HF}\), and label the molecular orbitals as bonding, antibonding, or nonbonding.

Short answer

The molecular orbital diagram for HF consists of one bonding orbital formed from the overlap of Hydrogen's 1s and Fluorine's 2s atomic orbital. The 2p atomic orbitals of Fluorine create nonbonding molecular orbitals as they do not overlap with Hydrogen's atomic orbital.

Step-by-step solution

Determining Atomic Orbitals

The first step is to determine the atomic orbitals of the involved atoms. Hydrogen has 1 electron in the 1s atomic orbital. Fluorine has 2 electrons in the 2s atomic orbital and 5 electrons in the 2p atomic orbitals (2px, 2py, and 2pz). Therefore, Fluorine has a total of 7 valence electrons.

Constructing Molecular Orbital Diagram

Now, construct a molecular orbital diagram. The hydrogen 1s atomic orbital can only interact with the 2s atomic orbital of Fluorine, forming a molecular orbital. The 2p atomic orbitals of Fluorine do not overlap with the Hydrogen's 1s and therefore are considered as nonbonding orbitals.

Filling Electron in Orbital

Begin filling electrons into the molecular orbitals. Follow the aufbau principle (lower energy levels are filled first), Pauli’s exclusion principle (maximum of two electrons can occupy an atomic orbital and they must have opposite spins) and Hund’s rule (if two or more orbitals have the same energy (degenerate), one electron goes into each until all are half full, the remaining electrons can then be paired up). The one electron from Hydrogen and the one electron from Fluorine's 2s atomic orbital fill up the bonding molecular orbital, and the remaining 6 electrons from Fluorine will fill up the nonbonding orbitals.

Labelling the Molecular Orbitals

The final step is to label the molecular orbitals. The molecular orbital formed from the overlap of Hydrogen's 1s and Fluorine's 2s atomic orbital is a bonding orbital. The molecular orbitals formed from Fluorine's 2p atomic orbitals remain nonbonding as they do not overlap with anything.

Key concepts

Bonding and Antibonding Orbitals

In the context of molecular orbital (MO) theory, bonding and antibonding orbitals play crucial roles in molecular stability and interactions. When atomic orbitals overlap, they can form molecular orbitals that are lower in energy, known as bonding orbitals, or higher in energy, termed antibonding orbitals.
Bonding orbitals, as seen in the overlap between hydrogen's 1s orbital and fluorine's 2s orbital in HF, lead to a stabilizing interaction where electron density is concentrated between the two nuclei. This increased electron density holds the nuclei together.
Antibonding orbitals are formed when the wave functions of overlapping atomic orbitals have opposite phases, leading to a node—a region of zero electron density. This results in a repulsive interaction that can weaken the bond between nuclei. However, in the case of HF, the molecular orbital formed from hydrogen's 1s and fluorine's 2s orbital is primarily a bonding orbital, while the 2p orbitals on fluorine remain nonbonding, as they do not overlap with any orbitals on hydrogen.

Aufbau Principle

The Aufbau Principle outlines the order in which electrons fill atomic orbitals in an atom or molecule, starting from the lowest to the highest energy level. In constructing molecular orbital diagrams, such as for HF, this principle is pivotal.
The principle guides us in filling the molecular orbitals formed by the atomic orbitals. We start by filling the lowest energy orbitals first. For HF, this means placing electrons in the bonding molecular orbital created from the combination of hydrogen's 1s and fluorine's 2s atomic orbitals before moving to higher energy levels.
This approach ensures that the molecule is as stable as possible with the available electrons, avoiding unnecessary high-energy states that wouldn't contribute to stability. In essence, following the Aufbau Principle ensures that the molecular structure is energetically efficient.

Pauli's Exclusion Principle

Pauli's Exclusion Principle is a fundamental concept that restricts the arrangement of electrons within orbitals. It states that no two electrons in an atom or molecule can have the same set of all four quantum numbers. This principle is crucial when filling molecular orbitals, including those in the HF molecule.
In practical terms, this means each molecular orbital can hold a maximum of two electrons, and they must have opposite spins (usually denoted as \(\uparrow\) and \(\downarrow\)).
For the HF molecule, this means that once the bonding molecular orbital is formed, it can accommodate two electrons—one from hydrogen and one from fluorine—with opposite spins. This ensures the electrons are distributed in a manner that respects the quantum constraints defined by the Pauli principle.

Hund's Rule

Hund's Rule is a guiding principle for electron configuration within orbitals, particularly useful when dealing with degenerate orbitals—those of the same energy level. According to Hund's Rule, electrons will first occupy each degenerate orbital singly before pairing up. This minimizes electron-electron repulsions and stabilizes the molecule.
In the context of HF, this rule is less directly applied given that the molecule doesn't have degenerate orbitals filled in the same manner as, say, multi-electron atoms with larger numbers of electrons filling multiple \(p\) orbitals.
However, its application becomes clear in other molecules where degenerate orbitals exist, such as when dealing with molecules involving multiple bonds that split into several energy levels. It ensures that the molecular orbital diagram reflects the least energetically costly configuration.