# Question #aa3cf

May 26, 2016

Plenty, but at the general chemistry level, copper and chromium are the most common "exceptions" and the ones you should definitely know.

The exceptions listed in my textbook that give nonstandard configurations are:

• $\textcolor{b l u e}{\text{Cr}}$ (chromium), $\textcolor{b l u e}{\left[A r\right] 4 {s}^{1} 3 {d}^{5}}$
• $\textcolor{b l u e}{\text{Cu}}$ (copper), $\textcolor{b l u e}{\left[A r\right] 4 {s}^{1} 3 {d}^{10}}$
• $\text{Nb}$ (niobium), $\left[K r\right] 5 {s}^{1} 4 {d}^{4}$
• $\textcolor{b l u e}{\text{Mo}}$ (molybdenum), $\textcolor{b l u e}{\left[K r\right] 5 {s}^{1} 4 {d}^{5}}$
• $\text{Ru}$ (ruthenium), $\left[K r\right] 5 {s}^{1} 4 {d}^{7}$
• $\text{Rh}$ (rhodium), $\left[K r\right] 5 {s}^{1} 4 {d}^{8}$
• $\text{Pd}$ (palladium), $\left[K r\right] 4 {d}^{10}$
• $\textcolor{b l u e}{\text{Ag}}$ (silver), $\textcolor{b l u e}{\left[K r\right] 5 {s}^{1} 4 {d}^{10}}$
• $\text{La}$ (lanthanum), $\left[X e\right] 6 {s}^{2} 5 {d}^{1}$
• $\text{Ce}$ (cerium), $\left[X e\right] 6 {s}^{2} 4 {f}^{1} 5 {d}^{1}$
• $\text{Gd}$ (gadolinium), $\left[X e\right] 6 {s}^{2} 4 {f}^{7} 5 {d}^{1}$
• $\text{Pt}$ (platinum), $\left[X e\right] 6 {s}^{2} 4 {f}^{14} 5 {d}^{9}$
• $\textcolor{b l u e}{\text{Au}}$ (gold), $\textcolor{b l u e}{\left[X e\right] 6 {s}^{2} 4 {f}^{14} 5 {d}^{10}}$
• $\text{Ac}$ (actinium), $\left[R n\right] 7 {s}^{2} 6 {d}^{1}$
• $\text{Th}$ (thorium), $\left[R n\right] 7 {s}^{2} 6 {d}^{2}$
• $\text{Pa}$ (protactinium), $\left[R n\right] 7 {s}^{2} 5 {f}^{2} 6 {d}^{1}$
• $\text{U}$ (uranium), $\left[R n\right] 7 {s}^{2} 5 {f}^{3} 6 {d}^{1}$
• $\text{Np}$ (neptunium), $\left[R n\right] 7 {s}^{2} 5 {f}^{4} 6 {d}^{1}$
• $\text{Cm}$ (curium), $\left[R n\right] 7 {s}^{2} 5 {f}^{7} 6 {d}^{1}$
• $\text{Lr}$ (lawrencium), $\left[R n\right] 7 {s}^{2} 5 {f}^{14} 6 {d}^{0} 7 {p}^{1}$
• $\text{Ds}$ (dermstadtium), $\left[R n\right] 7 {s}^{1} 5 {f}^{14} 6 {d}^{9}$
• $\textcolor{b l u e}{\text{Rg}}$ (roentgenium), $\textcolor{b l u e}{\left[R n\right] 7 {s}^{1} 5 {f}^{14} 6 {d}^{10}}$

Obviously, you do not have to memorize all of these. Just a few of them, which I will go into below.

Many of these "exceptions" follow different principles that are seemingly conflicting, so not all of these are "half-filled $n s$ subshell" configurations.

For many transition metals, the $n s$ orbital is higher in energy than the $\left(n - 1\right) d$ orbitals. That's why their $4 s$ electron is commonly removed for their first ionization.

Only a few exceptions, like yttrium ($\text{Y}$) and several $f$-block metals, have the $n s$ orbital (at least a little bit) lower in energy than the $\left(n - 1\right) d$ orbitals. You can see this in Appendix B.9 here.

Since copper and chromium both have one electron left until a filled $3 d$ subshell (whether singly-occupied or doubly-occupied):

• By Hund's rule to maximize the total number of parallel electrons ("one at a time and double up" is how I was first taught it), demotion of a $4 s$ electron down to a lower-energy $3 d$ orbital for chromium gives its more stable electron configuration by reducing the electron repulsion.
• Due to energy arguments, demotion of a $4 s$ electron down to a lower-energy $3 d$ orbital for copper gives its more stable electron configuration purely due to the difference in orbital potential energies ($\text{5.05 eV}$, or $\text{487.25 kJ/mol}$). The total number of parallel electrons, however, remains the same, so Hund's rule isn't applicable here.

The elements that follow similar principles in their electron configurations (giving a resultant half-filled $n s$, and filled $\left(n - 1\right) d$) as chromium and copper are:

• $\text{Mo}$, but not $\text{W}$ and not $\text{Sg}$!, each below $\text{Cr}$
• $\text{Ag}$, $\text{Au}$, and $\text{Rg}$, each below $\text{Cu}$

Note that these are not easily explainable, so you do not have to know why these configurations yield half-filled $n s$ subshells.

Any half-decent explanation should involve a complicated mixture of Hund's rule, energy differences between the $n s$ and $\left(n - 1\right) d$ subshells, and the increasing size of the $\left(n - 1\right) d$ or $\left(n - 2\right) f$ subshell for higher $n$ decreasing the electron repulsions and allowing paired electrons to be in possibly unexpected orbitals.