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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).
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.WFPM WFPM ( talk) 02:10, 29 August 2008 (UTC)
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:
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)
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)
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)
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)
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.
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)
"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."
"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."
"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."
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)
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)
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.
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)
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)
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)
Why is this a representation of the Aufbau principle. I don't see it.
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, ml and ms , 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)
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)
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:
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)
Surely the correct place for this link (if anywhere) is alternative periodic table. Physchim62 (talk) 00:40, 1 November 2008 (UTC)
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)
When I search the term "diagonal rule" it ought to bring me to this article.
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.
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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)
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)
I’ve tried to make clear that this is a metaphor. Is that better? Sandbh ( talk) 01:41, 17 July 2019 (UTC)
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)
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)
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)
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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).
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.WFPM WFPM ( talk) 02:10, 29 August 2008 (UTC)
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:
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)
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)
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)
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)
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.
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)
"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."
"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."
"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."
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)
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)
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.
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)
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)
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)
Why is this a representation of the Aufbau principle. I don't see it.
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, ml and ms , 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)
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)
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:
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)
Surely the correct place for this link (if anywhere) is alternative periodic table. Physchim62 (talk) 00:40, 1 November 2008 (UTC)
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)
When I search the term "diagonal rule" it ought to bring me to this article.
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.
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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)
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)
I’ve tried to make clear that this is a metaphor. Is that better? Sandbh ( talk) 01:41, 17 July 2019 (UTC)
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)
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)
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)