Module 3: Electron Configuration - Hund's Rule

Hund's Rule is a fundamental principle in quantum mechanics, specifically in atomic theory, that dictates how electrons populate degenerate orbitals within an atom.
It was previously discussed on Friday and is being revisited as a reminder of its importance in determining electron configurations.

Principle of Maximum Multiplicity: Hund's Rule states that for a given electron configuration, the term with the maximum multiplicity has the lowest energy. This often translates to a more intuitive rule for filling orbitals:
- When electrons are added to orbitals of the same energy (degenerate orbitals), each orbital is first occupied by a single electron before any pairing of electrons occurs.
- Furthermore, these single electrons in degenerate orbitals must have parallel spins (e.g., all spin up, or all spin down) to maximize the total spin angular momentum, which corresponds to maximum multiplicity.

Minimizing Electron-Electron Repulsion: The primary reason for Hund's Rule is to minimize the repulsive forces between electrons. By occupying separate degenerate orbitals with parallel spins, electrons are, on average, further apart from each other compared to being paired in the same orbital or in different orbitals with opposite spins.
Spin Correlation: Electrons with parallel spins tend to avoid each other more effectively (due to the Pauli exclusion principle requiring different spatial wavefunctions for electrons with parallel spins), thereby reducing electron-electron repulsion and lowering the overall energy of the atom.
Stability: Following Hund's Rule leads to the most stable (lowest energy) electron configuration for an atom. This is crucial for understanding an atom's chemical behavior and properties.

Let's consider the filling of p-orbitals, which are degenerate (having the same energy):

Carbon ($\ce{C}$), Atomic number $= 6$ :
- Electron configuration: $\text{1s}^2\text{2s}^2\text{2p}^2$
- For the two electrons in the $\text{2p}$ orbitals, Hund's Rule dictates:
 - $\text{2p}x^1$ $\text{2p}y^1$ $\text{2p}_z^0$ (with parallel spins, e.g., both up)
 - This is more stable than $\text{2p}x^2$ $\text{2p}y^0$ $\text{2p}z^0$ or $\text{2p}x^1$ $\text{2p}y^1$ $\text{2p}z^0$ (with anti-parallel spins).
Nitrogen ($\ce{N}$), Atomic number $= 7$ :
- Electron configuration: $\text{1s}^2\text{2s}^2\text{2p}^3$
- For the three electrons in the $\text{2p}$ orbitals, Hund's Rule dictates:
 - $\text{2p}x^1$ $\text{2p}y^1$ $\text{2p}_z^1$ (all with parallel spins)
 - This configuration makes nitrogen particularly stable due to the half-filled p-subshell.
Oxygen ($\ce{O}$), Atomic number $= 8$ :
- Electron configuration: $\text{1s}^2\text{2s}^2\text{2p}^4$
- For the four electrons in the $\text{2p}$ orbitals, Hund's Rule dictates:
 - First, one electron in each of $\text{2p}x$ , $\text{2p}y$ , $\text{2p}_z$ (with parallel spins).
 - The fourth electron will then pair up in one of the $\text{2p}$ orbitals, for example: $\text{2p}x^2$ $\text{2p}y^1$ $\text{2p}_z^1$

Aufbau Principle: Hund's Rule complements the Aufbau principle, which states that electrons fill lower-energy orbitals first before filling higher-energy ones.
Pauli Exclusion Principle: Hund's Rule works in conjunction with the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of four quantum numbers ( $n$ , $l$ , $ml$ , $ms$ ). This implies that if two electrons occupy the same orbital, they must have opposite spins.

Magnetic Properties: Hund's Rule helps explain the magnetic properties of atoms. Atoms with unpaired electrons (following Hund's Rule) are paramagnetic, meaning they are attracted to an external magnetic field. Atoms with all paired electrons are diamagnetic.
Spectroscopy: Understanding electron configurations based on Hund's Rule is essential for interpreting atomic spectra and understanding how atoms interact with light or other forms of electromagnetic radiation.
Chemical Reactivity: The most stable ground state electron configuration, determined by Hund's Rule, influences the number of valence electrons and thus an atom's chemical reactivity and bonding behavior.