# Which lanthanides are exceptions to the Aufbau principle?

Aug 24, 2017

See here for a fuller explanation on the lanthanides and actinides.

The order by atomic number is down the first column, and then down the second column. In $\textcolor{red}{\text{red}}$ are the 'Aufbau exceptions'.

$\textcolor{w h i t e}{\left[\begin{matrix}\textcolor{red}{L a} & \left(\textcolor{red}{\left[X e\right] 6 {s}^{2} 5 {d}^{1}}\right) & \textcolor{b l a c k}{T b} & \left(\textcolor{b l a c k}{\left[X e\right] 6 {s}^{2} 4 {f}^{9}}\right) \\ \textcolor{red}{C e} & \left(\textcolor{red}{\left[X e\right] 6 {s}^{2} 4 {f}^{1} 5 {d}^{1}}\right) & \textcolor{b l a c k}{D y} & \left(\textcolor{b l a c k}{\left[X e\right] 6 {s}^{2} 4 {f}^{10}}\right) \\ \textcolor{b l a c k}{P r} & \left(\textcolor{b l a c k}{\left[X e\right] 6 {s}^{2} 4 {f}^{3}}\right) & \textcolor{b l a c k}{H o} & \left(\textcolor{b l a c k}{\left[X e\right] 6 {s}^{2} 4 {f}^{11}}\right) \\ \textcolor{b l a c k}{N d} & \left(\textcolor{b l a c k}{\left[X e\right] 6 {s}^{2} 4 {f}^{4}}\right) & \textcolor{b l a c k}{E r} & \left(\textcolor{b l a c k}{\left[X e\right] 6 {s}^{2} 4 {f}^{12}}\right) \\ \textcolor{b l a c k}{P m} & \left(\textcolor{b l a c k}{\left[X e\right] 6 {s}^{2} 4 {f}^{5}}\right) & \textcolor{b l a c k}{T m} & \left(\textcolor{b l a c k}{\left[X e\right] 6 {s}^{2} 4 {f}^{13}}\right) \\ \textcolor{b l a c k}{S m} & \left(\textcolor{b l a c k}{\left[X e\right] 6 {s}^{2} 4 {f}^{6}}\right) & \textcolor{b l a c k}{Y b} & \left(\textcolor{b l a c k}{\left[X e\right] 6 {s}^{2} 4 {f}^{14}}\right) \\ \textcolor{b l a c k}{E u} & \left(\textcolor{b l a c k}{\left[X e\right] 6 {s}^{2} 4 {f}^{7}}\right) & \textcolor{b l a c k}{L u} & \left(\textcolor{b l a c k}{\left[X e\right] 6 {s}^{2} 4 {f}^{14} 5 {d}^{1}}\right) \\ \textcolor{red}{G d} & \left(\textcolor{red}{\left[X e\right] 6 {s}^{2} 4 {f}^{7} 5 {d}^{1}}\right) & \text{ & }\end{matrix}\right]}$

Generally the electron configuration exceptions occur

• early in the lanthanide series (lanthanum, cerium)
• after filling the $4 f$ orbitals halfway (gadolinium).

In general, it has to do with the closeness in energy of the $4 f$, $5 d$, and $6 s$ orbitals. The $5 d$ and $6 s$ are nearly the same energy across the entire lanthanide row, and the $4 f$ is fairly close in energy for the first few lanthanides.

That gives rise to the following rationales:

• $\text{La}$ and $\text{Ce}$ have an electron in their $5 d$ instead of $4 f$ because the $4 f$ is more radially compact, and given the small difference in energy between them (about $\text{6.8 eV}$), it is more energetically favorable to choose the $5 d$, which is radially more diffuse.

• $\text{Gd}$ has about a $\text{16 eV}$ $4 f - 5 d$ energy gap, and apparently, the electron repulsion it would generate to add another $4 f$ electron, combined with the radial compactness of the $4 f$ orbitals, is enough that it would rather have that electron in the $5 d$.