Talk:Aufbau principle

Possible Erratum

The proposed change would be consistent with my understanding of the orbital sequence table and would be consistent with the summary formula presented in the paragraph. change from: back to the s-block again for potassium and calcium (4s1, 4s2), and finally to the d-block for scandium (4d1). change to: back to the s-block again for potassium and calcium (4s1, 4s2), and finally to the d-block for scandium (3d1).

Yes, you're right. I fixed it. Thanks for the catch! Jon the Geek July 5, 2005 22:03 (UTC)

Division of cubic space

I didn't know there was so much lore about the electron orbital space locations but I've thought about a hierarchial process of dividing cubic space around a center point and would like to express an opinion. Which is that cubic space can be considered as either an accumulation of spheric spaces or as an accumulation of cubic volumes and in the case of atomic orbital volumes we assume that the volumes be analyzed and accumulated are cubic volumes. So in the case of the volume around the center of the atom we cut the big cube into three parts in all three orthogonal directional directions and can wind up with 27 equal small cubes within the big cube which can be numbered from 1 to 27 with number number 14 being the center small cube. Then there is a space hierarchy in the proximity of the small cubes to the central cubes consisting in decreasing proximity; (1) the 6 side connected cubes, (2) the 12 edge connected cubes, and (3) the 8 corner connected cubes. Now you would think that a partition of the space around the center of an atom or whatever would be partitioned in accordance with some logical consideration of these subordinate cubic space volumes but but they dont and give me doubts about there physical practicality.WFPMWFPM (talk) 02:10, 29 August 2008 (UTC)

Semantics Regarding Madelung Rule

I'm afraid I'm a little confused about the way the part of the article dealing with exceptions is phrased. In particular, the following section seems vague:

"Copper and chromium are common exceptions to the Aufbau principle:

Elemental copper should have 9 electrons in 3d orbital. But, its electronic configuration is [Ar].3d¹⁰.4s¹ instead of [Ar].3d⁹.4s² due to the greater stability of a half-filled than fully-filled orbital. Similarly, chromium takes the electronic configuration of [Ar].3d⁵.4s¹ instead of [Ar].3d⁴4s².

However, both copper and chromium comply with the Madelung (n+l) rule:

In all four cases presented above for the both elements: n+l=5, because the last, determining electron is located in 3d orbital. This would be more apparent if the electronic configurations were written in the order of the orbital filling: [Ar].4s¹.3d¹⁰ for copper and [Ar].4s¹.3d⁵ for chromium."

How can copper (for instance) "comply with the Madelung rule", when it clearly places an electron in 3d (n+l = 3+2 = 5) before finishing 4s (n+l = 4+0 = 4)? I mean, I understand the principle of finding greater stability with the half-filled d-shell. But semantically, isn't this still a violation of the Madelung rule? What does the "last, determing electron" have to do with anything? Isn't this just a question of orbital energy?

Thanks, Rundquist (talk) 02:08, 8 July 2008 (UTC)

Well, I went ahead and modified the article in order to conform to the information presented in the electron configuration article. The section I removed is given in my initial post above, in case anyone wants to incorporate it back into the article. Thanks, Rundquist (talk) 16:45, 19 July 2008 (UTC)

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I disagree with your edit, because the electron that makes Cu and Cr different from the previous elements is 3d electron, that makes n+l=5. This is why Cr and Cu are listed among transition metals, not among Alkali. There is another element that has 4s1 electron, that is Potassium. The element preceding Cr is V, it already has both 4s electrons (4s subshell already filled), therefore in Cr, the added electron, that makes all the difference, is in 3d subshell, same as in V (and not as in Na). Also, this 3d electron, will be the first to go during the oxidation. Agreed? Therefore, Cr and Cu are not exclusions to "n+l" rule, but exclusions to the Aufbau process, which is more about addition of the proton-electron pairs one-by-one , that does not occur naturally.

In accordance with the definition of the Madelung Rule presented in this article: "Orbitals are filled according to the n+l rule (also known as the Madelung rule after Erwin Madelung), where orbitals with a lower n+l value are filled before those with higher n+l values." And this is exactly what happens in Cr and Cu, and other elements that are regarded as exceptions when the protons are already in place.

Electron configurations can be written in at least three different ways. On the other hand, the Madelung rule is the basic rule of the Periodic Law. It should not be based on the way we show the electron configurations. The Madelung rule is more about distinction between the elements, not anything else. And, we all agree, such distinction is real. The Periodic Table is about the distinct elements. We do not list the elements in the Periodic Table in accordance with the energy. The Madelung rule makes the Periodic Table periodic. The Aufbau process is a different story. It is purely hypotetical and has little to do with the reality.

I went ahead and undid your modification. Drova (talk) 20:54, 24 July 2008 (UTC)

Sorry, I guess I'm still not getting it. We agree that the Madelung rule states "orbitals with a lower n+l value are filled before those with higher n+l values", correct? And yet, copper has a spot available in 4s (n+l = 4) while at the same time having completely filled 3d (n+l = 5). Therefore, it filled an n+l=5 orbital before an n+l=4 one. How is this not an exception? Perhaps we just have different understandings about what the "Madelung rule" is--I thought of it as a hypothetical structure which predicts most of the elements' electron configurations, but not all of them. And I think this viewpoint is prevalent in the literature; take, for example, this paper: [1], which also claims there are deviations from the Madelung rule, and lists copper and chromium among them.

Indeed, by your logic, what about zinc? The configuration for zinc is [Ar] 4s² 3d¹⁰, while the configuration for copper is [Ar] 4s¹ 3d¹⁰. Thus, the distinction between copper and zinc is a single electron in the 4s orbital, with n+l=4, while copper's "determining electron" had n+l=5. Wouldn't this violate the Madelung rule, as you put it? Thanks, Rundquist (talk) 00:33, 25 July 2008 (UTC)

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In fact the electron configurations, as you show them, have little to do with the order of orbital filling, they are written in accordance with the increase of n=1, 2, 3... and l= 0, 1, 2.... The Madelung rule follows n=1, 2, 3... and l= n-1, n-2, ...1, 0, that is the opposite order of "l" than in the typical electron configurations. This is what makes "n+l" rule work, keeping it constant for each period. In regard to the zinc, again, it has "n+l=5", and it is in the same period in the periodic table with the Cu. Do you agree that the first electron to be lost during the oxidation of Zn or Cu is 3d¹⁰, and that happens for the reason of higher energy? So, in the case of Cu ion, what if all protons are in place and 3d¹⁰ is missing? If this one missing electron comes back will it go to 4s or to 3d, where it is missing from? This paradox is well known, in fact this article refers to the book of Eric Scerri, where it is discussed. In one case we are talking about ions, in another we are talking about addition of the proton and electron together, that is never the case, because the elements are born "naked", that is without the electrons, which are added later. Also, if elements, such as Zn (not Cu) are to be considered as an exception to the Madelung rule, there would be only five or six of them, instead of 18, because no Lanthanides or Actinides would be among them. You can check it out. 68.48.234.55 (talk) 03:50, 25 July 2008 (UTC)

To reply to your last comment first (just to clear things up a bit), I completely agree that Zn (and similar elements) should not be considered an exception. I was merely bringing it up as an example of the fact that no matter what definition you use, there are going to be exceptions of one kind or another. Furthermore, please don't think that just because I write the electron configurations in a certain order, it means I think that's the way they have to be filled. I am merely following the notational convention.

Also, I'm not quite sure what you mean when you say "keeping it constant for each period" (referring to the "n+l" rule). If you mean the "highest n+l value of any electron within the atom", that's not entirely correct, as the most energetic electron in the ground state of Be (for example) has n+l=2, while the most energetic electron in the ground state of B has n+l=3, and yet both are generally considered to be in period 2. Indeed, it seems to me that the Madelung Rule has only a tangential relationship to the structure of the periodic table, since an element always simply belongs to the period that corresponds to its highest shell (i.e., highest n-value, not its highest n+l value), at least in the standard form of the periodic table.

Finally, I'm not sure the ionization of electrons is always perfectly related to the Madelung Rule either. For instance, according to NIST, the ground state configuration of singly-ionized Zn is [Ar].3d¹⁰.4s¹ (from here: [2]), which means that the first electron to be pulled off is actually a 4s electron, not a 3d as you mentioned earlier. It is the same thing with Cu: the first electron to be removed is taken from the 4s orbital, not the 3d orbital (which can be seen from the fact that singly-ionized copper has a ground-state configuration of [Ar].3d¹⁰, as shown here: [3]).

And that is why I think the Madelung Rule is not based on "determining electrons", electron ionizations, or the structure of the periodic table. It is related to these things, but it is simply a principle that says that for a given atom, electrons will not be placed into an orbital with a higher "n+l" value when spots that have lower "n+l" values are still free. Thus, Cu and Cr would be exceptions. I hope this gives a good explanation of my perspective, Rundquist (talk) 04:34, 25 July 2008 (UTC)

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When I refered to the periods with the equal n+l value, I was talking in terms of Janet's LSPT (1928), that strictly follows n+l rule, so that all elements in single period have the same "n+l" value. The IUPAC PT actually follows neither "n+l" rule, nor the electron structure. We can argue where each electron goes (and in fact there is no consistency in this regard in the literature), I would not call the Madelung rule a "hypotetical" one. I agree with such term if we talk about about the Aufbau principle, because it is truly hypotetical. Without the Madelung rule there would be no periodicity, period. It is also consistent with the atomic number Z: Cu in the same neighbourhood with Sc and Zn and even if I list "n+l" values for those elements using your logic, the sequence would be: 5,5,5,4,5,5,5,5,4,5. 'n+l" never goes above 5, it only falls down in few instances, and, again, it does not even happen within the Lanthanides and Actinides. Therefore, it has to be pointed out that not all common exceptions in regard to the electronic structure are exceptions to the Madelung rule, at least half of them are not. 68.48.234.55 (talk) 11:37, 25 July 2008 (UTC)

I went ahead and made some changes to bring this discussion to some common ground. Drova (talk) 16:45, 25 July 2008 (UTC)

While I appreciate the clarification you made in the article regarding the electron "that makes each of those elements distinct from its predecessors", I still think it is a misinterpretation of the term "Madelung rule". Atoms don't have "n" and "l" numbers by themselves--in this context, these terms only apply to the electrons. Thus, atoms can't have a single "n+l" value; this term is solely a property of electron orbitals. And the fact remains that Cu (for instance) has in its ground state electrons which occupy 3d orbitals (where n+l=5) while there is still a free spot open in the 4s orbital (which has n+l=4) and is therefore an exception to the Madelung rule.

As a side note, exceptions do happen in the Lanthanoid and Actinoid series, when you apply the complete Madelung rule. So far in this discussion, we have been ignoring the second clause of the Madelung rule, which states that if the n+l values of available orbitals are equal, then the orbital with the lower "n" value is filled first. This is why the Madelung rule is sometimes notated as the (n+l,n) rule, as it states that orbitals are filled in the order of increasing n+l, and then if those values are equal, increasing n. So Cu violates the first part of the rule because it doesn't completely fill 4s (where n+l=4) before placing electrons in 3d (where n+l=5), while La violates the second part of the rule because it places an electron in 5d (where n+l=7, but n=5) before filling 4f (where we also have n+l=7, but this time n=4<5).

On a more general level, the "Aufbau principle" is the statement that the electron configuration of an element in its ground state can be determined (i.e., predicted) by simply filling orbitals that have consecutively higher energy levels and "building up" orbital by orbital until no electrons are left. It says nothing about which orbitals you can expect to have higher energy than each other: that is what the Madelung rule is for. The Madelung rule is simply how you apply the Aufbau principle. See, for example, this comment: [4] by Eric Scerri, who says there is basically "no difference" between the terms "Aufbau principle" and "Madelung rule", and calls the Madelung rule "just a convenient mnemonic for spelling out the aufbau". If we both agree that Cu is an exception to the Aufbau principle, doesn't it stand to reason that it must be an exception to the Madelung rule as well, since the Madelung rule is simply the implementation of the Aufbau principle?

Thanks, Rundquist (talk) 02:21, 26 July 2008 (UTC)

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I thought we are talking about "n+l" rule, or as regarded by most, the Madelung rule, which, in fact was discovered by Janet (1930) 6 years before Madelung discovered it. If we are talking about "n+l" rule, then there are no exceptions among the Lanthanides and Actinides. If you want to add "n" to the "n+l" rule and make it "n+l,n", then it is not the "n+l" rule anymore. It puts additional constraint on the original "n+l" rule, and , of course, the more constraints, the more exceptions we shall expect. It could be called the "Madelung plus" rule then.

I will never except the premise that the "n+l" rule is hypothetical. The Aufbau principle is about "building up" of atoms one step at the time, when protons are added to the nucleus and the electrons are added to the orbitals one by one. Therefore, Aufbau is narrow, it is truly hypothetical and does not reflect the natural process. On the other hand the "n+l" rule is about ordering of energies of the whole orbitals 1s<2s<2P<3s<3p<4s<3d<4p..., it is broader than the Aufbau and it depicts the nature of the orbitals correctly. If some electrons in few elements fall out of this order during the hypothetical Aufbauprinzip, it does not affect the order of orbital energies in general. Therefore, the "n+l" rule is the basic natural law.

In fact, Eric Scerri, absolutely correctly, defines the Periodic Law as three basic rules: 1) "n+l" rule; 2) Hunds rule; 3) Exclusion principle. He excludes the Aufbau from the Periodic Law and he does not call it "n+l,n" rule. Try to call "n+l" rule "hypothetical", and the Periodic Law collapses, because neither Hund's rule nor Pauli's principle can carry it. Therefore, I strongly belive that it is a mistake to consider the Madelung rule (that is "n+l" rule) "just an implementation of the Aufbau Principle", because the "n+l" rule is broader than the Aufbau and it is not hypothetical, talking in terms of orbital energies. This is what Eric Scerri actually said in [5] "No difference, except the n + l rule gives the actual order, which is read off the empirical data." Well, the exception, that the rule gives the actual order, which is read off the empirical data is not a trivial one. On the other hand the Aufbauprinzip has little to do with the natural order. This is exactly the point I am trying to make. I appreciate your points of view. I understand that you are trying to tie the "electronic configuration" article with this one. I am just doing my best to protect the most important rule of the Periodic Law from making "swiss cheese" out of it with the little exceptions to the hypothetical Aufbau. I hope that we can find a common ground? Lovely discussion. Regards! Drova (talk) 02:55, 27 July 2008 (UTC)

Perhaps I was too strong in using the word "hypothetical" earlier. I certainly didn't mean to imply that the Madelung rule had no basis in physical reality--indeed, it is a modification (to the earlier point of view that orbitals were filled simply in order of increasing n values) that had to be made in order to conform to the spectroscopic characteristics of each element. So it is very much based in physical observations. But that doesn't mean it can't have exceptions. Now, I agree with you that the Madelung rule is all about the energy order of orbitals. What I was trying to say earlier about the relationship between the terms "Aufbau principle" and "Madelung Rule" is that while the Madelung rule gives the specific order that we can expect the energy of electron orbitals to follow, the Aufbau principle is the more general idea that it's even possible to predict electron configuration if you know the order of orbital energies. The Aufbau principle states that the electron configuration of an element can be found (which is true most of the time) by simply placing electron after electron in the available orbital with lowest possible energy. The Madelung rule simply tells you what this order is. Maybe it's not possible to call one of these ideas any more "broad" or "narrow" than the other, but it certainly seems that they are related.

In regard to Eric Scerri's comment, I believe that when he said "actual order" he was talking about the fact that the order implied by the Madelung rule is based on experimental data, not derived from first principles of quantum mechanics. But again, this doesn't mean that he thought the Madelung rule has no exceptions. Indeed, in the commentary he provides here: [6] he says that "the Madelung rule shows as many as twenty exceptions, starting with the elements chromium and copper". That certainly sounds like he identifies the term "Madelung rule" as being the same for what I called the "n+l,n" rule earlier.

He's not the only one, either. Indeed, the very title of this paper: [7], "The Löwdin challenge: Origin of the n + l, n (Madelung) rule for filling the orbital configurations of the periodic table", seems to imply that the term "Madelung" is just another name for the "n+l,n" order of orbital filling. Other scientific sources which support the idea that the Madelung rule is the same thing as the "n+l,n" rule, and that it has many exceptions, are as follows:

• [8] The article I referenced in an earlier post, which states

  "The filling of atomic orbitals in neutral atoms is said...to follow the Madelung rule: orbitals are occupied in order of increasing values of the sum of their n and l quantum numbers; for orbitals with the same values of (n+l), the orbital with lowest n is occupied first. This rule generally predicts correctly the order in which the energy levels of neutral atoms are filled...For almost one-third of the 58 transition metals – 10 in the d-block and 9 in the f-block – the Madelung rule predicts ground state configurations that differ from those determined experimentally."

• [9] A google books result which states

  "Unlike elements of the s- and p-blocks, whose electron configurations follow the Madelung Rule, a number of elements of the d- and f-blocks exhibit well-known exceptions to the Rule, attributed, in part, to half- and full-subshell effects."

• [10] Here, a long series of orbitals are listed which correspond to what I have been calling the "n+l,n" order. After doing so, however, the comment is made that

  "It is noted that among 99 neutral atoms, there are 20 exceptions to the series (1) [19]. The series (l), often referred to as the Madelung-Klechkovskii series thus presents an approximate character."

On the other hand, I have not seen any scientific papers that refer to the Madelung rule as "the most important rule of the Periodic Law", that talk about "differentiating electrons", or that claim that it has no exceptions. This is why I have come to the conclusion that I presented in this discussion: the Madelung rule is simply a convenient way to predict the orbital energies of most ground-state atoms, but it has exceptions. And the Periodic Table itself isn't perfect, either; sometimes you expect elements to behave a certain way based on other elements in their group, but experiments show a different result (indeed, the Lanthanoids have long been thought to bear more resemblance to other elements in their period than they do to the corresponding Actinoids in their groups). Now, maybe there is a more broad, overarching rule of periodic law, perhaps involving n and l quantum numbers in a similar fashion, but if so, I don't think it is called the "Madelung rule", and I also think it might not belong in the present article, which, after all, is supposed to be about the Aufbau principle.

I hope this clears some things up. This is an interesting discussion, and I'm not trying to attack your position or anything like that, I just think that the general use of the term "Madelung rule" in the scientific literature differs a bit from what you have presented. Thanks, Rundquist (talk) 00:45, 28 July 2008 (UTC)

I am glad that you agree with me that the Madelung rule is "very much based in physical observations". I tend to agree with you that, either way you look at the Madelung rule, it has exceptions. So, I think this is the common ground. Therefore, I propose following. Let's remove my previous language about Cu, Cr as being no exception to the Mudelung rule and add a phrase that the Madelung rule is based on empirical data. I tend to concur with your notion that "maybe there is a more broad, overarching rule of periodic law, perhaps involving n and l quantum numbers in a similar fashion ... and ... it might not belong in the present article". Therefore, since you initiated this discussion, I offer you to do the changes, if you agree to include something in regard to the empirical chracter of the Madelung rule. Drova (talk) 01:33, 28 July 2008 (UTC)

Alright, I've made some changes. In addition to adding a description of the experimental basis of the Madelung rule and modifying the section on exceptions, I also added some other comments that came up in this discussion and tried to include a few of the references cited on this talk page. I hope you agree with these edits; feel free to modify the page further if you think further clarification is necessary. Thanks, Rundquist (talk) 00:00, 30 July 2008 (UTC)

I can live with your revision in general, however it reflects your passion with the electron configurations. It has a link to the electron configuration article, that should be it. Also, when you talk about exceptions, you link to the Periodic Table which does not clearly show such exceptions. For the person who already does not know what they are, it would be hard to find out using that PT. I counted only 20 exceptions shown on that PT (Lu is not among the exceptions) and you state that there are 21 of them? It would be better to link to the page that already has the list. Also, in accordance with my sources there are only 18 exceptions that everybody agree on and the list changes all the time, as clarifications are made. Pt, for example, is not listed in CRC "Handbook of Chemistry and Physics" as an exception, at least in the edition that I have. I'd like to hear your opinion on that. Drova (talk) 11:38, 30 July 2008 (UTC)

I agree that my edit was rather heavy on the discussion of electron configurations, but I thought that was appropriate since the Aufbau principle is a method of predicting electron configurations. Do you really think we should remove the following section?

Many of these occur because a d subshell that is half-filled or full (i.e., 5 or 10 electrons) is more stable than the s orbital belonging to the next shell, since electrons occupying the same orbital will repel slightly and raise the energy of the atom. Removing one electron, for instance from an s subshell, will alleviate this unfavorable pairing energy. Thus, it takes less energy to maintain an electron in a half-filled d subshell than a filled s subshell.

It seems to me that this explanation is quite important for many of the exceptions, and it seems a little odd to simply say "some exceptions occur" without detailing the reasoning behind such cases.

You are quite right that there are only 20 exceptions; sorry for the typo. That is an excellent point that it is difficult to pick out the exceptions on that periodic table unless you know what you're looking for--perhaps it would be better to simply list the exceptions, or to provide a table showing side-by-side the expected configuration and the actual configuration, so as to inform the reader which elements do not follow the pattern.

As far as platinum goes, I was not aware of any question regarding its configuration. The configuration listed on its article is [Xe].4f¹⁴.5d⁹.6s¹, while it seems to me that the Madelung rule would predict [Xe].4f¹⁴.5d⁸.6s², since the 5d orbital has n+l=7 while the 6s orbital has n+l=6 and should therefore be filled first. What does the CRC handbook provide? I believe much of the electron data on Wikipedia comes from NIST, and is available here: [11]. You said there might be only 18 exceptions; is the other one you're wondering about lawrencium? NIST lists that configuration as tentative, since it is based on theoretical calculations but experiments haven't been possible to date.

Thanks, Rundquist (talk) 22:25, 30 July 2008 (UTC)

Periodic table in CRC handbook lists Platinum configuration as -32-16-2, (not -32-17-1) and Lawrencium as 32-9-2. I've read somewhere (I believe that was Scerri's book) that NIST data is not always accurate. Also, I corresponded with Dr. Stewart of Oxford (author of "Chemical Galaxy") in this regard and he quoted some new source that did not have Pt and Lr among exceptions. I need to research this better.

In regard to you paragraph about exceptions, it just sounds "too technical". It would be better, if we just mention energy and/or nuclear charge as a reason and make the paragraph shorter. Something like this: "the reason for the exceptions in electron configuration is the staggering of certain orbitals due to the increase of nuclear charge, that makes those orbitals somewhat contracted." Or something short as that. For now I removed that long sentence and the reference to the PT that did not show exceptions directly, until we work it out. Meanwhile, I will try to find out more about the Pt, Lr and NIST. I just searched the web and found that there is no concensus in regard to the Pt configuration. For example 2008 edition of Columbia Encyclopedia does not have Pt as an exception [12]. I found few more sites that are in agreement with -32-16-2. Drova (talk) 02:28, 31 July 2008 (UTC)

Simons and Reuhrer appear to be spam

The article claims "In fact, it was formulated by Niels Bohr along with Simons, Wolfgang Pauli and Reuhrer.", but I find no one of that name in Wikipedia, and in Google it looks like stuff derived from here. This reference is already in the original version of this article from 2005-03-03 10:50. I tried googling "bohr simons pauli aufbau", but without success, and "Ruehrer" and "Ruhrer" also did not help. Heinrich Rohrer sounds far more plausible, but his autobiography does not mention it. PJTraill (talk) 16:51, 3 October 2008 (UTC)

Sorry, I misread the history, it does not appear until http://en.wikipedia.org/enwiki/w/index.php?title=Aufbau_principle&diff=212283663&oldid=211909146 by 122.161.83.146 , where it looks very like schoolboy spam. It is amended in http://en.wikipedia.org/enwiki/w/index.php?title=Aufbau_principle&diff=next&oldid=218158901 by 122.161.10.29 to reintroduce Bohr and Pauli, but without removing the junk, although the spelling is changed. It seems evident that "Simons" and "Reuhrer" are spam, and I am removing them. PJTraill (talk) 17:21, 3 October 2008 (UTC)

What is the German for "Aufbau principle"?

It is evidently not Aufbauprinzip, which is not an article such as http://de.wikipedia.org/wiki/Aufbauprinzip!

It is curious that this article does not have a German equivalent, and I get the impression that this is because "Aufbau principle" is a name for a collection of rules, formulated by different people at different times. Is this the case, and is there no German expression for the same idea? PJTraill (talk) 16:56, 3 October 2008 (UTC)

I always thought that Aufbauprinzip is the German word for Aufbau Principle. I can quote few books that refer to it under that name.Drova (talk) 01:46, 6 October 2008 (UTC)

Aufbauprinzip is used in German for this concept, but not as frequently as I expected German-language Google search. Atombau ("atom building")is much more common German-language Google search, and is the term originally used by Bohr. Perhaps the general meaning of Aufbau is too present for German speakers, in the same way that English-speakers don't use the term "construction principle" or "structure principle"… German Wikipedia describes the Aufbau principle at de:Elektronenkonfiguration in the section headed Auffüllen der Schalen ("Filling (up) of the shells"). Physchim62 (talk) 08:40, 6 October 2008 (UTC)

PerfectPeriodicTable

Why is this a representation of the Aufbau principle. I don't see it.

Also, why does the link not violate WP:ELNO#11, as a personal web site from a person not recognized as an expert. — Arthur Rubin (talk) 22:12, 29 October 2008 (UTC)

It's also original research and, as far as I can tell, pseudoscientific. I've cut the link again. --Killing Vector (talk) 23:30, 29 October 2008 (UTC)

How is this pseudoscientific? Please, be more specific.

68.48.234.55 (talk) 02:10, 30 October 2008 (UTC)

From pseudoscience: Pseudoscience is defined as a body of knowledge, methodology, belief, or practice that is claimed to be scientific or made to appear scientific, but does not adhere to the scientific method, lacks supporting evidence or plausibility, or otherwise lacks scientific status.

Well, first we've got statements like This is exactly what is wrong with the traditional periodic table that "cuts" the sequence of the elements in periods primarily on the basis of metallic/nonmetallic/inert properties and Mendeleev did not know about the quantum numbers, therefore, he had to use what was available to him at the time of his inquiry: atomic weights and the properties of the elements which indicate a basic misunderstanding of how periods arise (they're based on what we now understand to be electron orbitals) or of the history of the periodic table (Mendeleev's layout didn't look like the modern one at all), but that nonetheless adopt scientific trappings.

Then we've got statements like The quantum mechanics in its present state can not fully explain all intricacies of the Periodic System in part because the quantum numbers n, l, m_l and m_s , that describe electronic populations of the atoms, are not completely understood in terms of mathematics, which is plain wrong (the quantum numbers arise from the eigenvalues in spherical harmonics, which are well-understood) and therefore implausible.

Finally there's the lack of scientific status. As far as I can tell, Mr Tsimmerman's work has not been cited by anyone in the fields of chemistry or physics, nor is he himself a published, peer-reviewed author in those fields. Without supporters in the scientific community, it doesn't even meet the standard of fringe science. --Killing Vector (talk) 10:26, 30 October 2008 (UTC)

Adomah Periodic Table that is discussed here is based strictly on placing quantum numbers in order. In standard Periodic Table s, p, d and f blocks that correspond to the quantum number l=0, 1, 2, 3 are presented as s, f, d and p, and follows l=0, 3, 2, 1. That is why the standard Periodic Table can not be used for deriving electron configuration without help of the mnemonic diagram. It is demonstrated here that Adomah peiodic table can be used without such mnemonic. What is pseudoscientific about that? Besides, Adomah periodic table is based on LSPT that was around from at least 1928.

In accordance with the well known article of Dr.Eric Scerri in "Foundations of Chemistry" and others The quantum mechanics in its present state can not fully explain all intricacies of the Periodic System. It is also opinion of the Dr. Henry Bent of the University of Pittsburg in his recent book on LSPT.

Finally, there is a new book in Spanish (soon to be translated in English) entitled ""La tabla periodica 100 anos despues de la muerte de Mendeleiev" (ISBN: 958-655-530-5) by Ruben Dario Osorio Giraldo and Maria Victoria Alzate Cano, PhD printed recently in Colombia that devotes 3 pages to the ADOMAH PT and the Tetrahedron and recognizes it as therecommended PT formulation. I happened to have a copy of it. Also, there is article by Dr. Philip Stewart of Oxford that was recently submitted to "Foundations of Chemistry" magazine that referes to the Perfect PT web site. That is in addition to the reviews quoted at the web site itself.

Therefore, I believe that it is wrong to call Mr. Tsimmerman's work "pseudoscientific". I think that the link in question should remain.Drova (talk) 12:17, 30 October 2008 (UTC)

As stated on another page, this claim is unusual, and such claims need to be verified in a rigorous manner. The "foundations of chemistry" magazine does not appear, and I could be wrong here, to exist in any Australian university or national library. This is unlikely to be the case for any scientific, peer reviewed journal of repute. The search can be verified at libraries australia -- the following may not be a permalink, if so, conduct the search yourself -- [13]. Please provide DOIs or direct links to journal articles that support this claim. I have found the magazine. Has the article been accepted for publication and is available? Until then, we cannot use this reference. User A1 (talk) 12:56, 30 October 2008 (UTC)

OK, I have just finished a paper by P. Stewart (DOI 10.1007/s10698-007-9038), "A century on from Dmitrii Mendeleev: tables and spirals, noble gases and Nobel prizes". This is possibly not the paper in question, nevertheless, I shall proceed until corrected.

The paper does not refer to the aufbau principle, nor is Mr Tsimmerman referenced, nor does it mention close packing. It merely argues that the periodic table may hae more aesthetically and logically pleasing layouts, compared to the one with which many are familiar. Furthermore it proposes a renaming of isolated neutrons, such as in neutron sources as a "zeroth element". I don't think that it supports any form of geometrical underpinnings to observed chemical properties, merely it does the reverse, supporting chemical underpinnings to geometrical layouts -- a radically different and more widely accepted idea. This article, whilst an interesting read, is not supportive of that link in any way, as far as I read it. The only website referrred to in the paper is quoted in a foot note as, " It is amusing to note, given Mendeleev’s aversion to spiritualism, that the most popular website for the text of the 1904 article is one devoted to the occult", how the author determines "most popular" is a question unto itself ;)User A1 (talk)

I think the most damning bit of evidence, is the "peer review" section of that website, where the emails which are purportedly received from university graduates & Drs. Secondly, the email from one other "support" indicates that she would like to reference the website in her work -- I believe this is almost taboo in academic circles, due to the self-publishing nature of the internet. *IF* the concept appears up *DIRECTLY* in a journal article, please provide a reference. User A1 (talk) 13:44, 30 October 2008 (UTC)

The title of the Stewart's article is "Charles Janet: the unrecognized genius of the Periodic System" Submitted in late June. He refers to the web site in references and mentions it in the text under "After Janet". The book in Spanish that I mentioned is out. I hope that article is out by now, but even if it is not, such links are recommended to be avoided, but not disallowed completely. I think, based on the contents of the link, there is nothing wrong with it. The 3D image only enhances the representation of the Aufbau process. Drova (talk) 15:21, 30 October 2008 (UTC)

As far as I can see, the article has not been publishd. It does beggar the question as how you have seen a preprint of an unpublished work -- this is possible in four ways:

• You are the author of this un-published work
• You are a colleague or confidante of this author
• You are the webmaster of the website in question, and have been contacted the author.

Any of these would immediately place you in the bounds of WP:COI -- If I have missed a possiblity then feel free to correct me here.

To make things clear, here is a list of articles to which you are trying to add this link -- this is based upon your editing history:

• Close packed spheres
• Electron configuration
• Quantum number
• Group theory
• Periodic table

In addition to the invalidity of the link as already discussed by many editors, across multiple talk pages there exists a substantial push from yourself to include this web-page. Whilst I thank you for raising this at the talk page and discussing this in a civil manner, I think that aside from yourself, there is pretty much zero support for including this link, with many editors labelling the link as "psuedoscience", "fringe science" or otherwise discounting it.

I would, to avoid accusations of WP:SPAM, be not actively encouraging the use of this link in multiple articles. This has the side effect of fragmenting discussion, as well as placing you in a position where you may be accused of having some form of bias, or vested interest. User A1 (talk) 23:07, 30 October 2008 (UTC)

Although some labeled the link as "psuedoscience", "fringe science" or otherwise discounting it, no one was able to point to a single specific error in the link provided. And this is not surprising, because those who labeled the the Link in question are far from being experts in the Madelung rule. One of the above critics, who used such degrading labels contributed articles mostly on Beer and Fascism, which have nothing to do with the subject of this scientific article. Because of the fierce opposition from the above Wiki crowd, I am not going to insist on the link at this time, or other links associated with the Perfect PT, until the pending article, or articles, come out in the leading scientific publications that would refer to it. However, when that occurs, the links to the Electron Configurations and/or to the Quantum Numbers, should be restored, because they would most definitely benefit many.Drova (talk) 02:29, 31 October 2008 (UTC)

Note from User_A1 : The linked words "link" "Electron Configurations" and "Quantum Numbers" have been unlinked by myself -- it is clear what website is being referred to (earlier) -- we don't need it 5 times User A1 (talk) 00:21, 1 November 2008 (UTC)

Surely the correct place for this link (if anywhere) is alternative periodic table. Physchim62 (talk) 00:40, 1 November 2008 (UTC)

That would be a good approach. The article should be about Janet's Left Step Periodic Table (LSPT), 1928 formulation and the Adomah Periodic Table, which is the modified LSPT, would be presented there as the logical continuation. I think this would be the right approach, because there are numerous articles about Janet's table in scientific literature. But I would wait for the Dr. Stewart's pending article in Foundations of Chemistry, where he refers to the Perfect PT before I undertake such task.Drova (talk) 13:05, 2 November 2008 (UTC)

Drova, I have unlinked your comments again. When making comments, kindly refrain from linking to the site continuously -- such action does not correlate wit a well thought out discussion. Regards User A1 (talk) 21:34, 2 November 2008 (UTC)

Definition

I am suspicious of the definition of the aufbau principle given under the "History" section. While it is a common way to state the definition nowadays, I suspect the idea that electrons filled lower orbitals first would have been unremarkable to Bohr and Pauli, and unworthy of being a principle that needed to be "formulated." After all, such ideas stem directly from principles of statistical mechanics which had been developed in the previous century. Instead, it seems to me, the principle must have been focused on the fact that the "ladder" of orbitals to be filled was, for the most part, in the same order for different elements. This is not such an obvious result, as the energies and shielding involved are very different and, in fact, there are exceptions.

In this article, this definition is also not referenced, which makes me doubly suspicious. Could someone provide a reference to what Bohr and Pauli actually said? SarahLawrence Scott (talk) 02:05, 20 September 2009 (UTC)

Yes, the history is far more complicated than that little, almost throwaway comment would suggest!

Bohr developed (dare I say "built up") his Aufbau principle between 1921 and 1923. The classic paper is usually deemed to be a 1923 paper (so classic, in fact, that I can't quickly find the exact reference, but I keep on looking), but he had already spoken publically about it in a series of lectures in Göttingen in June 1922 and in his Nobel lecture of December 1922 (starts at the bottom of page 25 of the PDF). See Brown, Laurie M.; Pais, Abraham; Pippard, A. B. (1995), Twentieth Century Physics, vol. 1 (2nd ed.), New York: AIP Press, pp. 96–97, ISBN 0-7503-0310-7.

Pauli was present at the Göttingen lectures (it was the first time the two men had met), and he succinctly describes one of the problems with Bohr's idea in his own Nobel lecture from 1945: "The question, as to why all electrons for an atom in its ground state were not bound in the innermost shell, had already been emphasized by Bohr as a fundamental problem in his earlier works." This was the problem which Pauli resolved with his exclusion principle: Pauli, W. (1925), "Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren", Z. Phys., 31: 765–83, doi:10.1007/BF02980631.

You will see another problem with Bohr's idea if you look at the table on page 28 of the PDF file of his Nobel lecture: the numbers of electrons in each sub-shell are wrong! Neon has four electrons in the 2s orbitals and four electrons in the 2p orbitals… Pauli is usually – and wrongly – credited for solving this problem: as Pauli himself admits in the abstract (to make it even more prominent) to his 1925 paper, the correct mathematical relationship between the numbers of electrons in each sub-shell was discovered by English physicist Edmund Stoner in 1924: Stoner, Edmund C. (1924), "The distribution of electrons among atomic levels", Phil. Mag. (6th Ser.), 48: 719–36.

So was Bohr's and Pauli's Aufbauprinzip the same as the one we use today? In essence, yes, as we can see from Bohr's Nobel lecture. Bohr realized early on that the order of of orbital energies, at least in highly ionized atoms, didn't depend on the charge on the nucleus: this is still held to be true today. However the postulate that became known as the Aufbauprinzip in the early years was the formalism from Bohr's 1923 paper, that the relative energy of orbitals isn't affected by the addition of electrons (the "permanence of quantum numbers" is how Pauli puts it). It soon became apparent that this is only an approximation, which is why we have Madelung's rule and exceptions to Madelung's rule. Physchim62 (talk) 13:11, 20 September 2009 (UTC)

This is also called the "diagonal rule"

When I search the term "diagonal rule" it ought to bring me to this article.

Above edit by 70.112.31.144 on 2013 Nov 06.

This is a good suggestion as many teachers use this name informally. I have now added a redirect here from Diagonal rule, and also mentioned the name diagonal rule in the article, with a source. Dirac66 (talk) 22:19, 8 November 2013 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Aufbau principle/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Comment(s)

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I really believe that the following sentences have to be cleaned up: "Elemental copper should have 11 electrons in the outermost shell. But, its electronic configuration is [Ar].3d10.4s1 instead of [Ar].3d9.4s2 due to the greater stability of a half-filled or fully-filled orbital. Similarly, chromium takes the electronic configuration of [Ar].3d5.4s1 instead of [Ar].3d4.4s2." Actually, elemental copper should have 9 electrons in 3d subshell and it has 10 instead. In both examples ([Ar].3d10.4s1 and [Ar].3d9.4s2) it has (not "should have") 11 electrons in 4th shell N. Also, what phrase "due to the greater stability of a half-filled or fully-filled orbital" mean? Shouldn't it be "due to the greater stability of a half-filled than fully-filled 4s orbital" instead? Also, the article states that the Madelung (n+l) Rule is "Generally" followed. It is followed in all cases. This is the basis for the periodic law. (n+l) rule is followed even in regard to the elements that are regarded as exceptions. Just look at the diagram on the same page. For both, copper and chromium, as well as the elements located next to them in the Periodic Table n+l=5 for the outer most electron. Drova (talk) 12:11, 26 May 2008 (UTC)

Last edited at 12:11, 26 May 2008 (UTC). Substituted at 08:35, 29 April 2016 (UTC)

Leaving order vs. filling order

@Double sharp:

Could you explain the reason for changing the configurations in the Madelung rule section from filling order (based on sequences of neutral atoms such as K, Ca, Sc, Ti, V, Cr) to leaving order (based on ionization sequences such as Cr, Cr⁺, Cr²⁺, Cr³⁺, ...)? From the viewpoint of quantum mechanics, 3d⁵4s¹ and 4s¹3d⁵ are completely equivalent. But from a pedagogical viewpoint, the Madelung rule describes the sequence of configurations of neutral atoms, so I think it is clearer to write the configurations in order of filling neutral atoms. Dirac66 (talk) 00:23, 9 December 2018 (UTC)

@Dirac66: Unless I am very much mistaken, it has always been standard to write them in leaving order; at least, that's what I remember from school (even when the Madelung rule was being taught). Greenwood and Earnshaw, for example, writes them all in leaving order, and that's also how they appear in all our element infoboxes. Double sharp (talk) 00:37, 11 December 2018 (UTC)

@Double sharp: Thank you. Some books do use filling order, such as Miessler and Tarr (2nd ed, p.38). To help readers who may have seen filling order elsewhere, I suggest we start with one atom which is not an exception (say Ti) and mention that both notations (3d²4s² and 4s²3d²) are equivalent, with a link to Electron configuration#Notation for more explanation. Then we can use only leaving order for all the exceptions. Dirac66 (talk) 18:20, 11 December 2018 (UTC)

@Double sharp: OK, done. As an example of a book using leaving order, I used Jolly because I don't own Greenwood and Earnshaw. Dirac66 (talk) 01:57, 2 January 2019 (UTC)

Exceptions as turbulence along a flight path

I recently edited this article to clear up some terminological confusion.

There also seemed to be confusion as to the status of the Madelung Rule. Is it an approximation? Is it a rule? Do some of the elements have anomalous configurations or is it the Madelung Rule that has anomalies?

Certainly the elements in question are not anomalous. Their electron configurations are an outcome of the interaction of Nature’s laws. These laws are thought to be elegant but the outcome of their interactions are usually not elegant given the irregularities we see in the world all around us.

The Madelung Rule is unusual. Sure it does not correctly predict the electron configurations of 20 elements out of 118. But if you arrange the elements in one long line and then count forward comparing the actual configurations with those predicted by the Madelung Rule you will see that after each incorrect electron configuration or configurations the Madelung Rule returns to predicting the right electron configuration. If the MR was a true approximation it should always be off by a small margin, or after scoring some early successes it should go further and further off target. But it doesn’t behave like that.

The only way I’ve been able to explain what is occurring is by way of a metaphor: “These exceptions [to the Madelung Rule] can be viewed as turbulence along a flight path; once passed the flight path returns to normal.”

It seems like the MR is the spine of the periodic table in terms of the electron configurations of the elements. There are some kinks along the way due to some unaccounted for additional interactions between the rules of Nature. But the core is there.

The literature on the nature of the Madelung Rule is effectively non-existent.

All of the above is based on my reading of the literature on the Madelung Rule, and discussions with chemists, and periodic table researchers and aficionados.

If anyone has a better way of clarifying the nature of the MR so as to clear up the folklore and misunderstandings about it, feel free to chime in.

I believe this is not OR as I doubt it would be challenged, since if it was removed, it would make the explanation of the MR less clear. I also feel this is a case meriting we ignore the OR rule, if that’d be called for, and as there is scope for doing. Sandbh (talk) 12:25, 13 July 2019 (UTC)

Sorry, but unless you can find a reliable textbook or scientific paper which relates electron configurations to turbulence and flight paths, the analogy must be considered as original research. I have found a brief discussion in Jolly's inorganic text, with a mention of a paper by D.P.Wong in Journal of Chemical Education on the topic. I will include these sources in the article as a start. Dirac66 (talk) 01:38, 16 July 2019 (UTC)

I’ve tried to make clear that this is a metaphor. Is that better? Sandbh (talk) 01:41, 17 July 2019 (UTC)

Equivalent Madelung/diagonal rule for spherical atomic nuclei

The classical electronic Madelung rule becomes apparent when the periodic table's periods are laid out in a Left-Step manner, after Charles Janet, from the late 1920's. In this depiction the order of appearance of each new orbital type in turn is the primary motivation rather than surface chemical behavior. The s-block elements thus appear on the RIGHT edge of the table, so the sequence is: 1s, 2s; 2p3s, 3p4s; 3d4p5s, 4d5p6s; 4f5d6p7s, 5f6d7p8s. The n+l rule shows that for each orbital in these recast periods, the sum is always the same within any one period.

The spherical atomic nucleus, under a simple quantum harmonic oscillator model (probably also what motivates the Janet Left-Step periodic table), also shows a left-step motif-the individual orbitals contain the same number of particles as the electronic ones.

The sequence is numbered differently by convention: 1s, 1p; 1d2s, 1f2p; 1g2d3s, 1h2f3p; 1h2g3d4s; 1j2h3f4p- this is because, unlike the electronic system, all the orbitals within a shell here are of the same parity. In the electronic left-step system, each period/shell length occurs twice: 2,2; 8,8; 18,18; 32,32. In the spherical nuclear system, on the other hand, it is the number of ORBITALS within a shell that occurs twice: 1,1; 2,2; 3,3; 4,4. In electronic periods/shells orbital parity alternates.

With the spherical nuclear shells, the equivalent of the Madelung rule is 2n+l rather than n+l as in the electronic system.

1s> 2(1)+0=2; 1p> 2(1)+1=3; 1d2s> 1d> 2(1)+2=4, 2s> 2(2)+0=4; 1f2p> 1f> 2(1)+3=5 2p> 2(2)+1=5; 1g2d3s> 1g> 2(1)+4=6, 2d> 2(2)+2=6, 3s> 2(3)+0=6; 1h2f3p> 1h> 2(1)+5=7, 2f> 2(2)+3=7, 3p> 2(3)+1=7; 1i2g3d4s> 1i> 2(1)+6=8, 2g> 2(2)+4=8, 3d> 2(3)+2=8, 4s> 2(4)+0=8; 1j2h3f4p> 1j> 2(1)+7=9, 2h> 2(2)+5=9, 3f> 2(3)+3=9, 4p> 2(4)+1=9.

Ellipsoidally deformed harmonic oscillator nuclei have different shell structures from that of a sphere, but the Madelung rule analogue is still based on the one outlined above, but with corrections. These corrections themselves are based on the oscillator ratio of the deformed nucleus, which determines how many times each orbital size are used, and their relative placements in the shell structure.

2601:89:C601:C3B0:4D70:9AF6:620E:94F6 (talk) 18:11, 24 May 2021 (UTC)

"Uncle Wiggly path"

Is "Uncle Wiggly path" actually in widespread use (at least in education), or is it just one guy's joke that happened to end up in a journal article from the 60s (or 80s)? If it's the latter, then I think its inclusion here is unencylcopedic and undue. Also, should it be "Uncle Wiggily" in reference to the children's book character? And is the information for the reference even correct? The doi takes me to an article from the 1980s by a different author. – Scyrme (talk) 20:36, 9 February 2023 (UTC)

Yes, I agree with you. This is a childish name which is not used seriously, and I will now delete it from the article. The other names given are more scientific. Dirac66 (talk) 21:14, 9 February 2023 (UTC)

Fair enough. I didn't want to just cut it immediately, since I saw that it's been listed in the article for a number of years (since 2019) and didn't want to cut something that might be helpful to young students (assuming use in schools, perhaps in North America), but I was probably being too cautious. – Scyrme (talk) 22:03, 9 February 2023 (UTC)

Agree. If it is indeed used in schools, we need a citation for that anyway. Qflib, aka KeeYou Flib (talk) 04:16, 11 February 2023 (UTC)

Reference for "Aufbau principle"

The Jolly book calls this thing the "Madelung rule". What is the ref which calls it "Aufbau"? Johnjbarton (talk) 17:36, 23 February 2024 (UTC)

Ok I found several and added one to the article. Bohr came up with the empirical rules but his atom model struggled to match them. Pauli's exclusion helped. Madelung was based on Thomas fermi atom. Johnjbarton (talk) 18:13, 23 February 2024 (UTC)