What causes odd electron configurations in elements like Cu, Cr, Ag, and Au?

[Chemist@]

What causes that some elements have an electron configuration that is not in agreement with Hund's rule (Cu, Cr, Ag, Au...)? E.g. why does chromine have a valent electron configuration of 4s¹ 3d⁵ instead of 4s² 3d⁴. The former configuration is said to be more energetically favored, but why?

 

[ZapperZ]

What causes that some elements have an electron configuration that is not in agreement with Hund's rule (Cu, Cr, Ag, Au...)? E.g. why does chromine have a valent electron configuration of 4s¹ 3d⁵ instead of 4s² 3d⁴. The former configuration is said to be more energetically favored, but why?

The simplest answer here is that if you look at the two orbitals (4s and 3d), the 3d, on average, is further away from the nucleus than then 4s. Thus, the 3d is shielded more from the nucleus, and thus, will have a higher energy than the 4s orbital.

Zz.

 

[Chemist@]

3d has higher energy, but why is it filled before 4s becomes completely filled?

I don't need the simplest answer, I need the answer that is nearest to the truth. I'd like a quantum mechanical explanation.

 

[ZapperZ]

3d has higher energy, but why is it filled before 4s becomes completely filled?

I don't need the simplest answer, I need the answer that is nearest to the truth. I'd like a quantum mechanical explanation.

But that's the point, 3d does NOT have a higher energy! If it does, it won't get filled up ahead of the 4s! It is closer to the nucleus than the 4s on average!

That is the QM explanation. If you don't care for it, solve the Schrodinger equation.

Zz.

 

[Chemist@]

In vanadium, 4s is filled before 3d(!), what causes the difference between Mn and Cr orbital filling?

 

[ZapperZ]

In vanadium, 4s is filled before 3d(!)

Yeah? Isn't that what we have been discussing all along? I feel like I keep having to repeat the same thing.

, what causes the difference between Mn and Cr orbital filling?

I'm confused. What is it exactly that you are asking? Mn and Cr have different number of electrons. Why should they have the same "orbital filling"?

Zz.

 

[Chemist@]

Okay, I will reformulate my quesiton:
Vanadium has a completely filled 4s orbital and 3 electrons in the 3d orbital, by analogy, chromine should be 4s² 3d⁴, but instead it is 4s¹ 3d⁵. Why isn't the 4s orbital in chromine filled completely?

 

[ZapperZ]

Okay, I will reformulate my quesiton:
Vanadium has a completely filled 4s orbital and 3 electrons in the 3d orbital, by analogy, chromine should be 4s² 3d⁴, but instead it is 4s¹ 3d⁵. Why isn't the 4s orbital in chromine filled completely?

Obviously, it is a lower energy to half-filled the 3d orbital than to fully fill the 4s orbital.

At some point, we simply can no longer simply try to give a hand-waving explanation on why this occurs, because the physics of multi-electron system gets rather complex. Anything beyond Helium will require sophisticated methods, such as DFT, to get the solution to such atoms.

Zz.

 

[Chemist@]

"At some point, we simply can no longer simply try to give a hand-waving explanation on why this occurs, because the physics of multi-electron system gets rather complex. Anything beyond Helium will require sophisticated methods, such as DFT, to get the solution to such atoms."

That's what I was asking for. Thank you for the answer.

 

[DrDu]

Maybe a simple explanation is that advancing along a period, the effective nuclear charge seen by the valence electrons increases as the valence electrons are not very effective in shielding each other from the nuclear charge. Compare the Slater rules Slater's rules - Wikipedia, the free encyclopedia.
Now with increasing (effective) nuclear charge, e.g. in going from V to Cr, the effects of many electron effects in an atomic problem become less pronounced and the ordering of the orbitals approaches that found in a hydrogen atom, i.e. 3d falls below 4s.
This is formalized using "Z expansion".