Niobium's 5s subshell unfilled?

[DocZaius]

Niobium: 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s1 4d4

I have been learning a little about electron configuration rules and from what I have read online, I cannot understand why Niobium doesn't fill its 5s subshell before moving on to the 4d subshell.

Wikipedia says "A d subshell that is half-filled or full (ie 5 or 10 electrons) is more stable than the s subshell of the next shell. This is the case because it takes less energy to maintain an electron in a half-filled d subshell than a filled s subshell."

That's all well and good but withholding an electron from the 5s subshell in this case doesn't give the 4d subshell 5 electrons! So what's the actual reason for the 5s subshell not being filled?

 

[Gokul43201]

Niobium is just a little weird. The ordering rules used for determining any electron configuration must be understood as nothing more than useful rules of thumb, but there are several exceptions, and Nb is one of them.

For a somewhat unilluminating reason with no predictive power, consider that 5s2 4d3 may be more energetic than 5s1 4d4 because the energy savings from dropping a 4d electron into a 5s sub-shell does not make up for the energy gain in having two spin-paired electrons in the same sub-shell. Clearly, this is not the case in either V or Ta, so it must be that the energy difference between 4d and 5s is smaller than the energy difference between 3d and 4s or between 5d and 6s.

 

[DocZaius]

Niobium is just a little weird. The ordering rules used for determining any electron configuration must be understood as nothing more than useful rules of thumb, but there are several exceptions, and Nb is one of them.

For a somewhat unilluminating reason with no predictive power, consider that 5s2 4d3 may be more energetic than 5s1 4d4 because the energy savings from dropping a 4d electron into a 5s sub-shell does not make up for the energy gain in having two spin-paired electrons in the same sub-shell. Clearly, this is not the case in either V or Ta, so it must be that the energy difference between 4d and 5s is smaller than the energy difference between 3d and 4s or between 5d and 6s.

Is there a clear set of rules (no matter how complicated) that actually accounts for all of these exceptions and is compatible with all the elements? If so, can it be found on the web?

 

[jungwirsch]

Oh no, you really don't want to go there. Or at least not before finishing a master's degree in Theoretical Chemistry or Particle Physics or the like. "No matter how complicated" would include the generation of a generalized wave function including the core and all electrons for all elements (anything less is an approximation and therefore will generate exceptions). It may well never have been done so far.

Want for a clear set of rules that needs no exceptions is a common source of frustration for those in introductory chemistry. All sets of rules (including, but by no means limited to, the rules for determining electron configurations) that are commonly taught in chemistry are based on one or the other set of simplifications, so they are never good for all cases. The real (quantum mechanical) situation is almost invariably so complex that simple rules do not exist. One who can accept that can go on to become a great chemist. One who cannot will eventually turn away from the subject. Sad, but true

 

[Borek]

This is an old thread, but as it was already revived - there is a simple rule. It states that ground state configuration is that of the lowest energy. It is calculation of the exact energy for any possible state that is tricky.

 

[jungwirsch]

This is an old thread, but as it was already revived - there is a simple rule. It states that ground state configuration is that of the lowest energy. It is calculation of the exact energy for any possible state that is tricky.

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And what exactly are you trying to say?

 

[Borek]

More or less the same you have said "Rule of lowest energy" is simple to state and understand, but of no use in practice, as it leads to hard to solve PDE. But the principle is simple.