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As cited in an answer to this question, the ground state electronic configuration of Niobium is:

Nb: [Kr] 5s1 4d4

Why is that so? What factors stabilize this configuration, compared to the obvious 5s2 4d3 (Aufbau principle), or the otherwise possible 5s0 4d5 (half-filled shell).

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it is a nice question – NewAlexandria Oct 29 '12 at 15:37
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5s subshell here has lower energy, then 4d subshell. However, there is non-zero energy of electron pairing on same orbital. So, we have one electron on 5s subshell and another is pushed onto 4d subshell. ||| do not overestimate these so-known 'principles', they work in most cases, true, but can fail dramatically on border cases, like this one where energy gap between two orbitals is not so big. ||| I do not post this as answer as I cannot prove my point by math or reference, it is a guess. – permeakra Nov 3 '12 at 13:41
@permeakra yeah, but if you follow this simple logic, there's no reason not to push two electrons into the d shell :) Hence the reason I ask how this can explained, which will most possibly involve quantum chemistry calculations. – F'x♦ Nov 3 '12 at 13:57
@F'x It is repulsion of two electrons on same orbital that pushes one of them from 5S subshell. After one is pushed away, the other have no reason to move. – permeakra Nov 3 '12 at 13:59
From what I can remember, the names come from atomic spectral line studies. S stood for Sharp, P for Principal, D for Diffused, F for Fundamental, and anything after that is alphabetical. Something about the energies and where they fall all the spectral line if I am correct. Don't know much more detail than that!! So, to lessen the workload, we write the first chunk as [noble gas]. You track back to the most recent noble gas, and write it in brackets to say: 'everything this noble gas has and then...'. Example: [Ar]4s2 (Calcium) says "everything argon has, the way argon had it, AND 2 electrons – Susan Diaz Nov 9 '12 at 11:43
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2 Answers

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Unfortunately, the Aufbau rule cannot predict all electron configuration as it doesn't take into account electron-electron interactions. In the end the Aufbau is only a rule of thumb. Electronic levels have to be found using quantum calculations taking into account electron-electron interactions (not to mention spin orbit coupling). Therefore there is no simple or rational explanation for this.

References:

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The question of anomalous electronic configurations, meaning s1 or s0 in one case (Pd) is very badly explained in textbooks. For example the anomalous configuration of Cr, 3d5 4s1 is typically explained as being due to half-filled subshell stability. This is wrong for several reasons. First of all there is nothing especially stable about half-filled subshells. Secondly it does not explain the fact that many second transition series elements show anomalous configurations even though they do not possess half-filled subshells. The possession of a half-filled subshell is neither necessary nor sufficient for there to be an anomalous configuration. There are atoms that have hfss but do not have anomalous configurations and there are atoms that have anomalous configurations but do not have hfss. Conclusion the use of the hfss explanation is ad hoc and should be avoided. It so happens that Cr and just one other atom have both hfss AND show an anomalous configuration. But it cannot be generalized.

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