Will electrons pair up in an orbital only when all orbitals in different sub-levels have one electron?

1 Answer
Aug 26, 2017

Usually, yes, but not necessarily.


For a given n, different sublevels have differing l, where l = 0, 1, 2, . . . , n-1.

Hund's rule states that in order to maximize spin multiplicity, an atom usually fills one orbital at a time, and pairs up after every orbital of the same energy (or neighborhood of that energy) is half-filled.

Well, a counterexample is that thorium ("Th") has a 7s orbital that is pretty much the same energy as its 6d AND 5f orbitals (empty circle vs. empty triangle vs. filled diamond):

![http://onlinelibrary.wiley.com/doi/10.1002/9781118688304.ch8/summary, pp. 199 - 202](useruploads.socratic.org)

And yet, its electron configuration is:

color(blue)([Rn]7s^2 6d^2 5f^0)

rather than... (as lower n is usually lower in energy)

[Rn]7s^2 6d^0 5f^2
(Aufbau)

or... (as it decreases electron pairing interactions)

[Rn]7s^1 6d^3 5f^0
(Hund)

or even more seemingly reasonable... (as lower n is usually lower in energy)

[Rn]7s^1 6d^0 5f^3
(Aufbau + Hund)

And the reasoning behind that is the 5f orbitals are particularly compact compared to the 6d that "Th" would rather have [Rn] 7s^1 6d^2 rather than [Rn] 7s^1 5f^2, even though (or rather, BECAUSE) they are all pretty much the same energy.

The 6d orbitals are also apparently not so diffuse that a [Rn] 7s^1 6d^3 ends up being viable, so that the 7s being doubly-occupied leads to the lowest-energy ground-state thorium atom.