Violations of Hund's Rule

Main Question or Discussion Point

"Violations" of Hund's Rule

Given an electron configuration such as 1s2 2s2 2px2 2py1

(My apologies for not knowing how to insert subscripts and superscripts.)

This electron configuration is in violation of Hund’s Rule.

Is such a configuration “forbidden” and therefore impossible?

If it is possible for this configuration to exist as an “excited state,” i. e., a 2pz electron pairing up with the 2px electron, is there any physical evidence for its existence?

dougz

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MathematicalPhysicist
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can you explain your notation:"1s2 2s2 2px2 2py1"
what s,px,py stands for?

1s2 2s2 2px2 2py1

In the electron configuration notation 2s2, the first 2 indicates the second shell of an atom; the s refers to the subshell and also the atomic orbital in that shell. The second 2 (which should be a superscript) means that 2 electrons are found in the 2s orbital.

In the notations 2px2 and 2py1, again the first 2 indicates the second shell of an atom. The p refers to a subshell in the second shell; there are three equivalent atomic orbitals in that subshell, oriented along the x, y, and z axes. The proper notation should be p subscript x, p subscript y, and p subscript z.

The second 2 (a superscript) in 2px2 and the 1 (also a superscript) in 2py1 describe the number of electrons occupying these atomic orbitals.

According to Hund's rule, in a series of equivalent, degenerate atomic orbitals the lowest energy level is achieved when electrons with parallel electron spins are added one at a time to each of the equivalent orbitals. Pairing of electrons in a particular orbital is allowed only after each orbital has one electron in it.

I hope this helps.

dougz

1s2 2s2 2px2 2py1

In the electron configuration notation 2s2, the first 2 indicates the second shell of an atom; the s refers to the subshell and also the atomic orbital in that shell. The second 2 (which should be a superscript) means that 2 electrons are found in the 2s orbital.

In the notations 2px2 and 2py1, again the first 2 indicates the second shell of an atom. The p refers to a subshell in the second shell; there are three equivalent atomic orbitals in that subshell, oriented along the x, y, and z axes. The proper notation should be p subscript x, p subscript y, and p subscript z.

The second 2 (a superscript) in 2px2 and the 1 (also a superscript) in 2py1 describe the number of electrons occupying these atomic orbitals.

According to Hund's rule, in a series of equivalent, degenerate atomic orbitals the lowest energy level is achieved when electrons with parallel electron spins are added one at a time to each of the equivalent orbitals. Pairing of electrons in a particular orbital is allowed only after each orbital has one electron in it.

I hope this helps.

dougz

Hund's rule is sometimes violated because the orbitals the electrons 'should' be filling are more energetic than other configurations, due to effects caused by quantum mechanics and general relativity.

Hunds rules are empirically based and turns out to be true for almost cases, but in general they cannot be proven, and as well there are counter examples.

I see you have 7 electrons, but what is the binding force? Nitrogen nuce? model potential of some kind?
The exchange could in some rare cases cause violation, if you carry it out carefully.

Finally, this hydrogenic-like orbital filling model, is normally not a good and accurate way of describing the true electronic structure, but approximately its perhaps close enough. Some self-consistent Hartree-Fock could give you better orbitals.

alxm

I see you have 7 electrons, but what is the binding force? Nitrogen nuce? model potential of some kind?
I think it's safe to assume an atomic nucleus. I've never seen the s-p-d-f categorization be used for any other type of potential.

Finally, this hydrogenic-like orbital filling model, is normally not a good and accurate way of describing the true electronic structure, but approximately its perhaps close enough. Some self-consistent Hartree-Fock could give you better orbitals.
Okay. Now that's just plain silly. Obviously, any real calculation on real, interacting, electrons is better. But you can't do SCF calculations in your head! As for not being a good and accurate way, that's silly too. Nobody ever claimed it's a quantitatively accurate method. But it does give good qualitative results a lot of the time. MO theory (and LCAO) serve as a simple framework for rationalizing, categorizing and discussing electronic structure. (even if a pi-orbital looks nothing like the combination of p-orbitals MO theory depicts it as, it's still called a pi-orbital). Its so successful in fact, that you'll find it in every single modern general-chemistry textbook. And it has in fact had significant impact on chemistry, such as in the creation of the Woodward-Hoffman rules of concerted reactions in organic chemistry (which garnered a Nobel-prize)

So don't be such a physicist ;) Just because it's not a good approximation to the solution of the Schrödinger equation doesn't mean it's useless.

I think it's safe to assume an atomic nucleus. I've never seen the s-p-d-f categorization be used for any other type of potential.
Spuds if pug dish of pig (minus the vowels) gives the ordering of the shells in nuclei. So it's at least used in nuclei.