Aufbau Principle: Fill lower energy orbitals first.
Pauli Exclusion Principle: Max 2 electrons per orbital, with opposite spins.
Hund's Rule: For degenerate orbitals, fill each orbital with one electron of parallel spin before pairing.
Stability of Half-filled and Fully-filled d-orbitals:
- $d^5$ (half-filled) and $d^{10}$ (fully-filled) configurations are exceptionally stable due to symmetry and exchange energy.
- This often leads to exceptions in electron configurations (e.g., Cr: $[Ar]3d^54s^1$ instead of $3d^44s^2$; Cu: $[Ar]3d^{10}4s^1$ instead of $3d^94s^2$).

Elements with partially filled d-subshells in their common oxidation states.
Key Properties:
- Variable oxidation states.
- Formation of colored compounds (due to d-d electronic transitions).
- Paramagnetism (due to unpaired d-electrons).
- Good catalysts (due to variable oxidation states and ability to form coordination complexes).
- Formation of coordination compounds (ligands donate lone pairs to empty d-orbitals).
Crystal Field Theory (CFT) / Ligand Field Theory (LFT):
- Describes splitting of d-orbital degeneracy in coordination complexes.
- In an octahedral field, d-orbitals split into two sets: $t_{2g}$ (lower energy: $d_{xy}, d_{yz}, d_{xz}$) and $e_g$ (higher energy: $d_{x^2-y^2}, d_{z^2}$).
- The energy difference ($\Delta_o$) determines color and magnetic properties.

Exist for $n \ge 4$. (e.g., $4f, 5f, ...$)
For $l=3$, $m_l$ can be $-3, -2, -1, 0, +1, +2, +3$. This means there are 7 degenerate f-orbitals in a free atom.
Each f-orbital can hold 2 electrons, so an f-subshell can hold a maximum of 14 electrons.
Shapes are very complex and not typically memorized, often described as having multiple lobes.

Fill the $4f$ subshell.
Located after Barium (Ba) and before Hafnium (Hf).
Often have a stable $+3$ oxidation state.
Key Properties:
- Lanthanide Contraction: Poor shielding by $4f$ electrons leads to a smaller than expected atomic/ionic radius across the series, affecting subsequent elements.
- Generally less reactive than Group 1 and 2 metals.
- Compounds are often colored and luminescent (used in lasers, phosphors).
- Paramagnetic properties.

Fill the $5f$ subshell.
Located after Radium (Ra) and before Rutherfordium (Rf).
All are radioactive.
Exhibit a wider range of oxidation states than lanthanides (e.g., U: $+3, +4, +5, +6$).
Key Properties:
- Most are synthetic (transuranic elements).
- Used in nuclear energy and weapons.
- Poor shielding by $5f$ electrons also contributes to actinide contraction, but less pronounced and more complex due to relativistic effects.

Orbital Type	$l$ value	Min. $n$	Number of Orbitals	Max Electrons	Shape Complexity	Associated Elements