What is Hund's rule of maximum multiplicity?

Hund's rule of maximum multiplicity states that the lowest energy electron configuration in orbitals of equal energy (degenerate orbitals) is the one with the maximum number of unpaired electrons with parallel spins.

Here's a breakdown of what that means:

• Degenerate Orbitals: These are orbitals within the same subshell that have the same energy level. Examples include the three p orbitals (px, py, pz) or the five d orbitals.

• Maximum Multiplicity: Multiplicity is related to the number of unpaired electrons. Higher multiplicity means more unpaired electrons with the same spin.

• Parallel Spins: Electrons are said to have "spin," which can be either "spin-up" or "spin-down." Parallel spins mean that all the unpaired electrons in the degenerate orbitals have the same spin (either all spin-up or all spin-down).

In simpler terms: When filling degenerate orbitals, electrons will individually occupy each orbital before any orbital gets a second electron. And, these singly occupied orbitals will all have the same spin.

Why does this happen?

This rule is based on two factors:

1. Exchange Energy (or Exchange Interaction): This is a quantum mechanical effect that lowers the energy of the system when electrons with the same spin are exchanged between degenerate orbitals. This stabilization effect increases as the number of possible exchanges increases, which is maximized when electrons are unpaired and have the same spin.

2. Electron-Electron Repulsion: By occupying different orbitals, electrons minimize their spatial proximity to one another, thus reducing electron-electron repulsion. Pairing electrons in the same orbital increases this repulsion.

Example:

Consider filling the 2p orbitals of a carbon atom. Carbon has 6 electrons, so its electronic configuration is 1s²2s²2p². We need to determine how to arrange the two electrons in the 2p orbitals (2px, 2py, 2pz).

• According to Hund's Rule, the electrons will occupy two separate 2p orbitals with parallel spins. The correct configuration is 2px¹2py¹2pz⁰, with both electrons having the same spin. This is lower in energy than pairing the electrons in the same 2p orbital (e.g., 2px²2py⁰2pz⁰).

Why is this important?

Hund's rule is crucial for:

• Predicting the electronic configurations of atoms and ions.
• Understanding the magnetic properties of atoms and molecules. Unpaired electrons contribute to paramagnetism.
• Explaining chemical bonding and reactivity.