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I am reading a book about Advanced Chemistry, and it is discussing the subject of half-filled orbitals.

The book notes that Chromium has an electron structure of $1s^2 2s^2 2p^63s^23p^63d^54s^1$

There is also some added stability when a sub-shell is half-full as this minimises the mutual repulsion between pairs of electrons in full orbitals.

Now, I'm confused by this explanation.

Is it correct to conclude that if a sub-shell is half filled, the repulsion between electrons in the half-filled subshell and other subshells with fully-filled orbitals is reduced (e.g. between the $3d$ and $3p$ subshell in Chromium)?

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  • $\begingroup$ This refers to repulsions between electrons in the half-filled subshell. In this case, the 3d electrons repel each other less. $\endgroup$ – orthocresol♦ Sep 27 '17 at 19:35
  • $\begingroup$ @orthocresol so what's the reference to "repulsion between pairs of electrons in full orbitals"? $\endgroup$ – vik1245 Sep 27 '17 at 19:35
  • $\begingroup$ I don't actually know, so I'm confused too by the exact wording. The topic has been explained elsewhere: chemistry.stackexchange.com/questions/58625/… You may find it relevant. $\endgroup$ – orthocresol♦ Sep 27 '17 at 19:36
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I actually just had this in class, and it confused me as well. This site helped me to understand it a bit better: http://www.chemguide.co.uk/atoms/properties/3d4sproblem.html

The author, a retired chemistry professor, states:

"Many chemistry textbooks and teachers try to explain this by saying that the half-filled orbitals minimise repulsions, but that is a flawed, incomplete argument. You aren't taking into account the size of the energy gap between the lower energy 3d orbitals and the higher energy 4s orbital."

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