$Ce^{4+}$ (4$f^0$): Achieves noble-gas-like empty 4f configuration. $Ce^{4+}$ is a strong oxidising agent (E° for $Ce^{4+}$/$Ce^{3+}$ = +1.61V). CeO2 (ceria) used in self-cleaning ovens and automotive catalytic converters. $Eu^{2+}$ (4$f^7$): Achieves half-filled 4f stability. $Eu^{2+}$ is a reducing agent, similar to $Ba^{2+}$ in properties (similar ionic radius). EuSO4 is insoluble like BaSO4. $Yb^{2+}$ (4$f^{14}$): Achieves fully-filled 4f stability. Less common than $Ce^{4+}$ and $Eu^{2+}$. $Tb^{4+}$ (4$f^7$): Another half-filled configuration, but rare. These anomalous states arise from the extra stability of $f^0$, $f^7$, and $f^{14}$ configurations.