Hund's Rule, often referred to as Hund's Rule of Maximum Multiplicity, is a fundamental principle in quantum chemistry that dictates how electrons occupy orbitals within a subshell when multiple orbitals of equal energy (degenerate orbitals) are available. It states that:
- Every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied.
- All electrons in singly occupied orbitals have the same spin.
This rule ensures that the most stable, lowest-energy electron configuration (the ground state) is achieved for an atom.
Understanding the Core Principles
Hund's Rule is crucial for accurately predicting the electron configuration and, consequently, the chemical behavior and magnetic properties of elements. It can be broken down into two interconnected aspects:
1. Minimizing Electron-Electron Repulsion
Electrons are negatively charged and thus repel each other. When filling degenerate orbitals within a subshell (like the three p orbitals, five d orbitals, or seven f orbitals), electrons will spread out as much as possible, occupying each orbital singly before pairing up in any one orbital. This spatial separation minimizes the electrostatic repulsion between electrons, leading to a more stable atomic configuration. Imagine a group of people boarding a bus: they will first occupy individual seats before anyone sits next to another person, provided there are empty seats available.
2. Maximizing Spin Multiplicity
When electrons singly occupy orbitals, they tend to have parallel spins (e.g., all spin "up" or all spin "down"). This alignment of spins is energetically favorable because it maximizes the total spin multiplicity of the atom. According to quantum mechanics, electrons with parallel spins have a lower energy state compared to those with opposite spins in different orbitals. This phenomenon is related to exchange energy, a quantum mechanical effect that is maximized when electrons have parallel spins in different orbitals.
Illustrative Examples
Let's look at how Hund's Rule applies when filling p orbitals, which can hold a maximum of six electrons across three degenerate orbitals (px, py, pz). Each orbital is often represented by a box, and electrons by arrows (↑ for spin up, ↓ for spin down).
| Element | Atomic Number | Relevant Subshell | Electron Configuration (p-subshell) | Orbital Diagram (2p subshell) | Unpaired Electrons | Magnetic Property |
|---|---|---|---|---|---|---|
| Carbon (C) | 6 | 2p | 2p² | [ ↑ ] [ ↑ ] [ ] |
2 | Paramagnetic |
| Nitrogen (N) | 7 | 2p | 2p³ | [ ↑ ] [ ↑ ] [ ↑ ] |
3 | Paramagnetic |
| Oxygen (O) | 8 | 2p | 2p⁴ | [↑↓ ] [ ↑ ] [ ↑ ] |
2 | Paramagnetic |
Explanation of Examples:
- Carbon (C): Carbon has two electrons in its 2p subshell. Following Hund's Rule, these two electrons will occupy two different 2p orbitals, each with a parallel spin (e.g., both spin up).
- Nitrogen (N): Nitrogen has three electrons in its 2p subshell. Each of the three 2p orbitals will receive one electron, and all three electrons will have parallel spins, leading to three unpaired electrons.
- Oxygen (O): Oxygen has four electrons in its 2p subshell. The first three electrons will occupy the 2p orbitals singly with parallel spins, just like nitrogen. The fourth electron then pairs up with an electron in one of the 2p orbitals, but with an opposite spin, following the Pauli Exclusion Principle. This results in one paired orbital and two singly occupied orbitals with parallel spins.
Relationship with Other Principles
Hund's Rule works in conjunction with other fundamental principles of electron configuration:
- Aufbau Principle: States that electrons fill atomic orbitals of the lowest available energy levels before occupying higher energy levels.
- Pauli Exclusion Principle: States that no two electrons in an atom can have the exact same set of four quantum numbers. This means that if two electrons occupy the same orbital, they must have opposite spins (one spin up, one spin down).
Together, these rules provide a comprehensive framework for constructing accurate orbital diagrams and understanding the electronic structure of atoms.
