Fwd: New publisher full-text added to your publication.

[Larry T.]

This is what I received from ResearchGate. Until now that article was obscure and hard to find.

I am including PDF file for those in this PT group who do not have ResearchGate account.

New publisher full-text added to your publication. New publisher full-text added to your publication. ResearchGate and University of California Press have partnered in a program to give researchers new ways of accessing research content. As part of this program, University of California Press has provided a publisher version of one of your articles, which we've added to your publication's page. Using Hund’s Rule and Spin Multiplicity to Assess Competing Versions of Group 3 and f-Block Constituency Article   Full-text available December 2019 The Chemical Educator  Valery Tsimmerman ·  Conal Boyce The article explores Group 3 constituency and f-element representation. In considering those intertwined topics, we frame the discussion in terms of two varieties of periodic table: the one seen in most chemistry texts, where Group 3 is comprised of Sc-Y-La-Ac, and a lesser-known variety, where Group 3 is Sc-Y-Lu-Lr (which makes it akin to Janet’s Left-Step Periodic Table). We also discuss the type seen most often in physics texts, where Group 3 takes the form Sc-Y-*-**, thus footnoting La and Ac to join the other lanthanides/actinides. This variety we look at less closely since it may be regarded as a variant of the first type mentioned. From Hund's rule, spin multiplicity and ground-level microstate data we erect a framework for judging which of the types seems most attuned to atomic structure. Our conclusion is that the type with Sc-Y-Lu-Lr accords best; it possesses an f-block that ends, unequivocally, on the first 4f¹⁴ element (Yb). By contrast, the f-elements of the other two types pass through Yb to halt at the second 4f¹⁴ element (Lu), as if in a delayed reaction or stutter. View full-text This message was sent to val...@perfectperiodictable.com by ResearchGate. To make sure you receive our updates, add ResearchGate to your address book or safe list. See instructions If you don't want to receive these emails from ResearchGate in the future, please unsubscribe. ResearchGate GmbH, Chausseestr. 20, 10115 Berlin, Germany. Imprint. See our Privacy Policy and Terms of Service.

[René]

Thanks Larry. 

It’s mentioned by Google Scholar, too. 

Their entry isn't quite right since it shows nil citations whereas I cited your article in my group 3 FoC article.

I suppose this is timely reminder that we’re due for a periodic discussion on the composition of group 3.

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<Using_Hunds_Rule_and_Spin_Multiplicity_to_Assess_.pdf>

[René]

Larry

It’s interesting that the conclusion of your paper with Conal included the following:

By now, the reader will have noticed that our subtext is: "In a perfect world, we would not be comparing Types A/B/C at all since they would have been long since supplanted by Janet’s LST." Realising how unlikely it is that the LST might rise to such prominence in the foreseeable future, one’s attention turns to Type C as a compromise that might be practical.

[Type A = La in Group 3; Type B = */**; Type C = Lu in Group 3.]

I’ve been reflecting on the use of the term "compromise" in that context. IUPAC has itself explicitly characterised its table (Type B) as a compromise between two established conventions—namely, tables placing either La or Lu in Group 3. In that case, the compromise is between alternatives that already have a more or less comparable standing.

By contrast, framing Type C as a compromise between the conventional medium-long form tables and Janet’s left-step table seems like it’s standing on wobbly ground, since the left-step table lacks a comparable status.

René

On 30 Jan 2026, at 15:20, 'René' via Periodic table mailing list <PT...@googlegroups.com> wrote:

Thanks Larry. 

It’s mentioned by Google Scholar, too. 

To view this discussion visit https://groups.google.com/d/msgid/PT-L/2D5AA03E-BA17-47D0-84F6-460AEC8FCB34%40iinet.net.au.

[Larry T.]

Rene,

We were writing about a compromise between PT that is based on wobbly notion of "behavior" and PT that is based on fundamental property of all observable matter, such as spin.

 Without spin, that is responsible for atoms' electromagnetic interaction, nothing could stand on anything. You would fall through the floor of your home and keep falling through the planet Earth.

  The graphics in that paper clearly demonstrate that ignoring such things as total spin and multiplicity of atoms makes the whole block of the periodic system thrown off the pattern established by three other blocks.

 

  Anyway, thank you for the citation. I hope one day it will be reflected on ResearchGate page.

V.T.

[René]

Hi Larry

Thanks. I think we may be talking past one another slightly, so let me try to restate my point more clearly.

I understand that in your paper with Conal the LST is treated as the fundamental form, and that the Lu table is proposed as a practical compromise between the three chemistry tables (La, Lu, and IUPAC) and the LST, specifically because in the Lu form each block begins with multiplicity 2 and ends with multiplicity 0.

I also agree that, viewed purely in terms of spin multiplicity, the Lu form gives cleaner block starts and ends than the La form, where the f-block begins with multiplicities 1 and 3 and ends with 2 and 2.

My point is spectroscopic rather than philosophical.

Spin multiplicity is only one component of the atomic term symbol. When the full ground-state term symbols (2S+1, L, J) are considered, the Lu form actually introduces one additional mismatch relative to group/block expectations compared with the La form. In other words, Lu–Lr improves multiplicity regularity, but at the cost of overall term-symbol coherence.

So yes, Lu–Lr gives very neat block boundaries in terms of multiplicity, but when term symbols are taken as a whole (which are more encompassing than spin alone), the La–Ac arrangement ends up being slightly more regular.

In addition, the Lu form:

• has one more overall differentiating-electron anomaly than the La form; and
• represents the only case where a pair of elements assigned to the same column have no outer electrons in common with that block (and at its start, at that).

From my perspective, this suggests that the Lu form resolves one aspect of regularity while introducing several new irregularities elsewhere.

René

[Mario Rodriguez]

I want to share a thought while travelling on a bus, especially with René

One problem is actually we don't have a clear definition of what a block is, and there are 2 options:

1. We consider a block is defined by a predominant orbital throughout the period but allowing irregular starts in heavy atoms. The important feature is the overall fit should have the lowest mismatches with theoretical filling. So the f-block can start with La, Ac and Th (despite having d orbital), d-block can start in period 7 with Lr (despite having p orbital), and g-block can start from element 121 (despite also start filling a p orbital, if I remember well the predicted configurations)

2. You consider a block is defined strictly by their valence orbital. In that case, you have to consider La, Ac, and Th (altogether) makes a secondary d-block, Lr makes a secondary p block and after element 120, we wouldn't start the g-block but a kind of tertiary p block. In this case we have to redefine/redraw blocks as they are depicted nowadays.

What we cannot do is making an arbitrary distinction between La and Ac (d1) case compared to Th case (d2), and also Lr (p1) and the start of g-block. Or we assume blocks have irregular starts in heavy atoms or we have to create inserted secondary and even tertiary new blocks. Otherwise it would be an arbitrary distinction between identical situations. In other words, what you consider for La and Ac, you have to consider for Th as well (and the rest). I consider La, Ac and Th are irregular starts of the f-block. Do you consider La, Ac and Th (altogether) should be in the d-block instead? Because it's the only alternative logical option.

Mario Rodríguez Peña

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[Larry T.]

Hi René,

In your last email, you noted:

"Spin multiplicity is only one component of the atomic term symbol. When the full ground-state term symbols (2S+1, L, J) are considered, the Lu form actually introduces one additional mismatch relative to group/block expectations compared with the La form. In other words, Lu–Lr improves multiplicity regularity, but at the cost of overall term-symbol coherence."

Based on this, would you argue for including Sc, Y, La, Ac, and Lu in Group 3 for the sake of "term-symbol coherence"?

Term symbols are only consistent within groups belonging to the s-block and p-block; this "coherence" does not exist within the d-block and f-block groups. Given that, why would Group 3 be granted special status? If you include La and Ac in group 3, the f-block would begin with Ce and Th, creating the similar problem, only in the f-block instead of the d-block. Where is the improvement? If we stick with something as fundamental as electron spin, we can really see how the pattern emerges across all four blocks. 

Best regards,

Larry T.

[René]

On 10 Feb 2026, at 15:18, Larry T. <ora...@gmail.com> wrote:

Hi René,

In your last email, you noted:

"Spin multiplicity is only one component of the atomic term symbol. When the full ground-state term symbols (2S+1, L, J) are considered, the Lu form actually introduces one additional mismatch relative to group/block expectations compared with the La form. In other words, Lu–Lr improves multiplicity regularity, but at the cost of overall term-symbol coherence."

Based on this, would you argue for including Sc, Y, La, Ac, and Lu in Group 3 for the sake of "term-symbol coherence"?

Thanks Larry for your follow-on question.

I wouldn’t argue for Sc, Y, La, Ac and Lu in group 3. While they each have the same term symbol there’s not enough room in group 3 for five metals.

Term symbols are only consistent within groups belonging to the s-block and p-block; this "coherence" does not exist within the d-block and f-block groups.

That’s not quite right. For example, term symbols are consistent for groups 4, 7, 9, 11 and 12 in the d-block.

Given that, why would Group 3 be granted special status? If you include La and Ac in group 3, the f-block would begin with Ce and Th, creating the similar problem, only in the f-block instead of the d-block.

Group 3 doesn’t have any special status.

If La–Ac are included in Group 3, the term-symbol anomalies at the start of the f-block are Ce and Th–Np, and at the end are Lu–Lr, giving a total of seven.

This can be compared to an Lu table in which there is one term-symbol anomaly in the start of the d-block (Lr) and seven anomalies at the start of the f-block (La, Ce, Ac–Np), for a total of eight.

One may further reasonably regard initial term-symbol irregularities as more disruptive to block logic than terminal ones.

Where is the improvement?

There is no term-symbol anomaly in Group 3. There is one less differentiating-electron discrepancy.^ And the f-block does not begin with two elements having no outer electrons in common with that block—a stronger departure from block logic than any comparable irregularity elsewhere in the table.

^ As Eric and Bill Parsons wrote:

“…for the purpose of selecting an optimal periodic table we prefer to consider block membership as a global property in which we focus on the predominant differentiating electron.” (Scerri and Parsons 2018, p. 151).

Scerri ER & Parsons W, What elements belong in Group 3 of the periodic table? In Scerri E & Restrepo G (eds) Mendeleev to Oganesson: A multidisciplinary perspective on the periodic table, pp. 140–151, Oxford University Press, New York (2018)

If we stick with something as fundamental as electron spin, we can really see how the pattern emerges across all four blocks.

I agree about the pattern but it comes at the expense of letting the spin “tail” wag the dog of term symbols, differentiating electrons, and block logic.

While an La table results in a split d-block when presented in 32-column form everyone learns that 4f fills between 5d¹ and 5d². So seeing d¹ → f → d²–d¹⁰ on the table feels natural.

Best regards,

Larry T.

cheers, René

[René]

On 7 Feb 2026, at 01:56, 'Mario Rodriguez' via Periodic table mailing list <PT...@googlegroups.com> wrote:

I want to share a thought while travelling on a bus, especially with René

Thanks very much Mario for contributing your thoughts. It sounds like it was a fairly long bus trip?

One problem is actually we don't have a clear definition of what a block is, and there are 2 options:

1. We consider a block is defined by a predominant orbital throughout the period but allowing irregular starts in heavy atoms. The important feature is the overall fit should have the lowest mismatches with theoretical filling. So the f-block can start with La, Ac and Th (despite having d orbital), d-block can start in period 7 with Lr (despite having p orbital), and g-block can start from element 121 (despite also start filling a p orbital, if I remember well the predicted configurations)

I don’t think the definition of a block is especially problematic. The s-block, for example, is formed due to the differentiating electrons entering an s orbital. Moving to the right we encounter the f-block (disconnected under the main body of the table), the d-block and the p-block.

As Eric and Bill Parsons noted, "...for the purpose of selecting an optimal periodic table we prefer to consider block membership as a global property in which we focus on the predominant differentiating electron.” (Scerri and Parsons 2018, p. 151). As you said, "The important feature is the overall fit should have the lowest mismatches with theoretical filling."

On this basis, an La-Ac Group 3 table is more optimal, because it introduces one fewer differentiating-electron anomaly than an Lu-Lr table.

2. You consider a block is defined strictly by their valence orbital. In that case, you have to consider La, Ac, and Th (altogether) makes a secondary d-block, Lr makes a secondary p block and after element 120, we wouldn't start the g-block but a kind of tertiary p block. In this case we have to redefine/redraw blocks as they are depicted nowadays.

What we cannot do is making an arbitrary distinction between La and Ac (d1) case compared to Th case (d2), and also Lr (p1) and the start of g-block. Or we assume blocks have irregular starts in heavy atoms or we have to create inserted secondary and even tertiary new blocks. Otherwise it would be an arbitrary distinction between identical situations. In other words, what you consider for La and Ac, you have to consider for Th as well (and the rest). I consider La, Ac and Th are irregular starts of the f-block. Do you consider La, Ac and Th (altogether) should be in the d-block instead? Because it's the only alternative logical option.

No arbitrary distinction is being made.

The f-block begins with the first appearance of an f electron at Ce. Thorium with its d- differentiating electron represents an irregular start to the 5f row in the same way that Lr, if placed in group 3, would represent an irregular start to the 5d row.

The situations are not identical however since an La table has one less differentiating electron discrepancy.

In response to your question, there is no need to consider La, Ac and Th (altogether) being in the d-block instead.

Mario Rodríguez Peña

René

[ERIC SCERRI]

Since my work, with my former student Will Parsons, has been mentioned,

The labels of blocks of elements in the periodic table (s,p,d or f) refer to the differentiating electron, not the outermost electron, nor the most energetic electron in any particular atom.

For example, take scandium.  The correct configuration is [Ar] 3d1 4s2.   

The outermost electron is in an s-orbital, and the most energetic electron is also in an s-orbital.  

And yet Sc is classified as being an s-block element because the electron that differentiates it from the previous element, calcium [Ar] 4s2, is that 3d electron.

The only instances where this definition breaks down is with atoms having anomalous configurations.

Consider vanadium.   [Ar] 3d3 4s2 

and chromium            [Ar] 3d5 4s1.  

Here the difference lies both in the d orbital and well as an s orbital.  The notion of differentiating electron becomes ambiguous in all 20 or so anomalous atoms.  But this does not matter, just like the violations of the 

n + l rule don’t matter to the overall architecture of the periodic table.

Chemistry deals with inexact concepts such as the n + l rule, acidity, electronegativity, aromaticity, bonding etc., etc.

This is why I believe that attempts to resolve the group 3 debate, for example, should be decided through broad and general philosophical or conceptual arguments rather than looking at the minutiae of the elements in question, regardless of whether they be chemical, or concerned with spectroscopic term symbols, or what have you.

regards

Eric Scerri

ERIC SCERRI PhD

UCLA

Website: http://www.ericscerri.com
PhilPeople https://philpeople.org/profiles/eric-scerri
Google Scholar https://scholar.google.com/citations?hl=en&user=8w1T5bEAAAAJ
ResearchGate https://www.researchgate.net/profile/Eric-Scerri

Editor-in-Chief of Foundations of Chemistry https://link.springer.com/journal/10698

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[René]

On 23 Feb 2026, at 06:42, ERIC SCERRI <sce...@g.ucla.edu> wrote:

Since my work, with my former student Will Parsons, has been mentioned,

The labels of blocks of elements in the periodic table (s,p,d or f) refer to the differentiating electron, not the outermost electron, nor the most energetic electron in any particular atom.

Thanks Eric for confirming this approach for us. There were a couple of other points in your post that I’d appreciate some clarification on.

For example, take scandium.  The correct configuration is [Ar] 3d1 4s2.   

The outermost electron is in an s-orbital, and the most energetic electron is also in an s-orbital.  

And yet Sc is classified as being an s-block element because the electron that differentiates it from the previous element, calcium [Ar] 4s2, is that 3d electron.

The only instances where this definition breaks down is with atoms having anomalous configurations.

Consider vanadium.   [Ar] 3d3 4s2 

and chromium            [Ar] 3d5 4s1.  

Here the difference lies both in the d orbital and well as an s orbital.  The notion of differentiating electron becomes ambiguous in all 20 or so anomalous atoms.

I don’t quite see how the differentiating electron becomes “ambiguous” in anomalous atoms such as chromium. Thus:

"The changes which distinguish one element from its predecessor…may be attributed to the last electron added; this electron is referred to as the "differentiating electron."

Kleinberg J et al. 1960, Inorganic chemistry, DC Heath and Co., Boston, p. 62

On this basis, wouldn’t there then be six differentiating-electron discrepancies in the d-block if La is in group 3—namely Mn (s), Zn (s), Tc (s), Ag (s), Cd (s), and Hg (s)?

But this does not matter, just like the violations of the 

n + l rule don’t matter to the overall architecture of the periodic table.

Chemistry deals with inexact concepts such as the n + l rule, acidity, electronegativity, aromaticity, bonding etc., etc.

I agree chemistry makes use of many approximate or context-dependent concepts. But I think it’s too broad to characterise chemistry itself as fundamentally inexact.

Alongside these approximations, are there not exact concepts such as triads, valence, and chemical formulae (CO2 really is CO2 rather than being approximately so)? Even the n+l rule is exact on a recurring basis in that after each anomaly or sequence of such, the rule once again holds, until the occurence of the next anomaly (that's interesting behaviour for what's supposed to be an approximation).

And aren't quantum numbers themselves discrete, even if their chemical consequences are sometimes blurred?

This is why I believe that attempts to resolve the group 3 debate, for example, should be decided through broad and general philosophical or conceptual arguments rather than looking at the minutiae of the elements in question, regardless of whether they be chemical, or concerned with spectroscopic term symbols, or what have you.

Given the inexact and exact nature of chemistry, I’d see broad philosophical or conceptual arguments as framing the group 3 discussion rather than replacing engagement with the chemical and physical particulars. Otherwise there’s a risk of doing philosophy about chemistry while setting aside the very evidence that gives the periodic table its meaning. I was reminded of a related observation that you made in a 2021 book review:

"As philosophers we have a natural tendency to concentrate on generalities and not to get too involved in the specifics and the details. Above all else, this new book reminds us that such an approach needs to be tempered by a detailed knowledge of the exceptions and features that go against the simplified generalities which we so cherish."

Scerri E 2021, Book Review of Geoff Rayner-Canham: The periodic table: past present, and future, Foundations of Chemistry, vol. 23, pp. 293–295

Those words strike me as especially relevant here.

General principles matter—but don’t they work best when informed by, rather than detached from, the details?

cheers, René

[ERIC SCERRI]

On Feb 25, 2026, at 3:09 AM, René <re...@iinet.net.au> wrote:

On 23 Feb 2026, at 06:42, ERIC SCERRI <sce...@g.ucla.edu> wrote:

Since my work, with my former student Will Parsons, has been mentioned,

The labels of blocks of elements in the periodic table (s,p,d or f) refer to the differentiating electron, not the outermost electron, nor the most energetic electron in any particular atom.

Thanks Eric for confirming this approach for us. There were a couple of other points in your post that I’d appreciate some clarification on.

For example, take scandium.  The correct configuration is [Ar] 3d1 4s2.   

The outermost electron is in an s-orbital, and the most energetic electron is also in an s-orbital.  

And yet Sc is classified as being an s-block element because the electron that differentiates it from the previous element, calcium [Ar] 4s2, is that 3d electron.

The only instances where this definition breaks down is with atoms having anomalous configurations.

Consider vanadium.   [Ar] 3d3 4s2 

and chromium            [Ar] 3d5 4s1.  

Here the difference lies both in the d orbital and well as an s orbital.  The notion of differentiating electron becomes ambiguous in all 20 or so anomalous atoms.

I don’t quite see how the differentiating electron becomes “ambiguous” in anomalous atoms such as chromium. Thus:

"The changes which distinguish one element from its predecessor…may be attributed to the last electron added; this electron is referred to as the "differentiating electron."

Kleinberg J et al. 1960, Inorganic chemistry, DC Heath and Co., Boston, p. 62

Could it be that Kleinberg is wrong?  The last electron added to d block atoms are s-orbital electrons.

He was writing in the 60s before folks like Eugen Schwarz and myself had clarified the order of electron occupation in transition metal atoms.

On this basis, wouldn’t there then be six differentiating-electron discrepancies in the d-block if La is in group 3—namely Mn (s), Zn (s), Tc (s), Ag (s), Cd (s), and Hg (s)?

See above.

Regards

Eric Scerri

P.S.  I regret to announce the passing of Keith Taber who is known to some of you from the now defunct Chemical Education server.  

[René]

On 26 Feb 2026, at 04:21, ERIC SCERRI <sce...@g.ucla.edu> wrote:

For example, take scandium.  The correct configuration is [Ar] 3d1 4s2.   

The outermost electron is in an s-orbital, and the most energetic electron is also in an s-orbital.  

And yet Sc is classified as being an s-block element because the electron that differentiates it from the previous element, calcium [Ar] 4s2, is that 3d electron.

The only instances where this definition breaks down is with atoms having anomalous configurations.

Consider vanadium.   [Ar] 3d3 4s2 

and chromium            [Ar] 3d5 4s1.  

Here the difference lies both in the d orbital and well as an s orbital.  The notion of differentiating electron becomes ambiguous in all 20 or so anomalous atoms.

I don’t quite see how the differentiating electron becomes “ambiguous” in anomalous atoms such as chromium. Thus:

"The changes which distinguish one element from its predecessor…may be attributed to the last electron added; this electron is referred to as the "differentiating electron."

Kleinberg J et al. 1960, Inorganic chemistry, DC Heath and Co., Boston, p. 62

Could it be that Kleinberg is wrong?  The last electron added to d block atoms are s-orbital electrons.

He was writing in the 60s before folks like Eugen Schwarz and myself had clarified the order of electron occupation in transition metal atoms.

Kleinberg does not seem to me to be mistaken. He was referring to the difference between the electron configurations of Z and Z + 1, rather than to differences between the configurations of ions having the same value of Z.

In the case of Cr, the difference between V (3d3 4s2) and Cr (3d5 4s1) is +2d and −1s.

It would therefore appear that the last electron added is a d electron. There is also a redistribution involving an s electron, but that redistribution concerns the final ground-state arrangement rather than the identity of the electron added.

cheers, René

[René]

On 19 Feb 2026, at 02:00, Larry T. <ora...@gmail.com> wrote:

Rene,

You wrote: 

"I agree about the pattern but it comes at the expense of letting the spin “tail” wag the dog of term symbols".

You can argue that for placing La and Ac at the beginning of the block d rows, but you can't do so for the ends of the block rows, which have to end with ¹S_0. In this case, not only the spin, but the term symbols at the tails of the block rows wag whole blocks. So, the f-block needs to end with Yb and No 😊.

Dear Larry

That’s an interesting response where you wrote that block rows “have to end with ¹S₀.”

As far as I know, there is no rule or law mandating that block rows terminate in ¹S₀. If that is the case, then the f-block does not need to end with Yb–No.

If, however, the f-block is required to end with Yb–No, it must begin with La–Ac. That would create an unprecedented anomaly: it would be the only instance in the periodic table where a pair of elements assigned to the same column are placed in a block with which they share no outer electrons at all—and this would occur at the very start of the block. That seems a stronger departure from block logic than any comparable irregularity elsewhere. In that sense, singlet closure would be determining block structure rather than differentiating electrons.

Since a terminal irregularity may reasonably be regarded as less disruptive than an initial one, it seems more natural for the f-block to begin with Ce–Th, consistent with the inaugural appearance of an f electron in Ce. On this view, each block begins with the first appearance of its differentiating electron: s at H, p at B, d at Sc, and f at Ce.

It is true that Th lacks an f electron in its ground state—but Lr likewise lacks d character at the start of the 6d row in an Lu-in-Group-3 table. If the latter is tolerated, it is not obvious why the former should be decisive.

A concise way of putting this is that block beginnings are defining events, whereas block endings are contingent closures.

best regards, René

[ERIC SCERRI]

On Feb 26, 2026, at 2:55 AM, René <re...@iinet.net.au> wrote:

On 26 Feb 2026, at 04:21, ERIC SCERRI <sce...@g.ucla.edu> wrote:

For example, take scandium.  The correct configuration is [Ar] 3d1 4s2.   

The outermost electron is in an s-orbital, and the most energetic electron is also in an s-orbital.  

And yet Sc is classified as being an s-block element because the electron that differentiates it from the previous element, calcium [Ar] 4s2, is that 3d electron.

The only instances where this definition breaks down is with atoms having anomalous configurations.

Consider vanadium.   [Ar] 3d3 4s2 

and chromium            [Ar] 3d5 4s1.  

Here the difference lies both in the d orbital and well as an s orbital.  The notion of differentiating electron becomes ambiguous in all 20 or so anomalous atoms.

I don’t quite see how the differentiating electron becomes “ambiguous” in anomalous atoms such as chromium. Thus:

"The changes which distinguish one element from its predecessor…may be attributed to the last electron added; this electron is referred to as the "differentiating electron."

Kleinberg J et al. 1960, Inorganic chemistry, DC Heath and Co., Boston, p. 62

Could it be that Kleinberg is wrong?  The last electron added to d block atoms are s-orbital electrons.

He was writing in the 60s before folks like Eugen Schwarz and myself had clarified the order of electron occupation in transition metal atoms.

Kleinberg does not seem to me to be mistaken. He was referring to the difference between the electron configurations of Z and Z + 1, rather than to differences between the configurations of ions having the same value of Z.

In the case of Cr, the difference between V (3d3 4s2) and Cr (3d5 4s1) is +2d and −1s.

It would therefore appear that the last electron added is a d electron. There is also a redistribution involving an s electron, but that redistribution concerns the final ground-state arrangement rather than the identity of the electron added.

OK.  Let’s just agree to disagree.  

To me difference means either adding or subtracting!  

I think the move from V to Cr is therefore ambiguous regarding where the difference takes place since it is both in d and s orbitals.  

In any case why does this matter?

[Mario Rodriguez]

Hi René,

I love travelling because it “forces” me to step away from duties and gives me unhurried time to think, something that’s rare in the life of a lecturer. Even though I’m sure we won’t convince each other on this topic, I’d like to share a few concise points.

- Th can be seen as an "ideological Trojan horse" for Ac. If one accepts that Th (d²) can be placed in the f-block without having any electron in an f orbital, then the preceding logical element (d¹) can be placed there as well and, logically, must be. Your current classification of Ac (d¹) in the d-block and Th (d²) in the f-block is mainly because the element above Th, Ce, is not d², and including La, Ac, and Th altogether in the d-block would look awkward and aesthetically unappealing. Hence, the solution becomes to declare, somewhat arbitrarily, that Ac (d¹) is d-block because it has a d electron, while Th (d²) is an “irregular” f-block element because it has d electrons. The logical reasoning would be or both irregular in the f-block or both regular in the d-block.

- I was also surprised when you said (I think to Larry) that it is “logical” for an f-block to lie between d¹ and d². There is, in fact, no f-block between Ac (d¹) and Th (d²). At the same time, in your response to Eric, you praised the validity of the n + l rule. According to that rule, there is no d¹ stage between filling the s and f orbitals: the sequence is simply s → f → d.

- What I meant by “The important feature is the overall fit should have the lowest mismatches with theoretical filling” refers to the table I already sent you, which has not been falsified yet:

 La    Ce      Pr      Nd     Pm     Sm     Eu     Gd      Tb,     Dy      Ho       Er       Tm        Yb       Lu

Real                               d1   d1 f1    f3       f4       f5       f6       f7    f7 d1     f9      f10      f11       f12      f13       f14    f14 d1

Starting with d1 then f    d1   d1 f1  d1 f2  d1 f3  d1 f4  d1 f5  d1 f6  d1 f7  d1 f8  d1 f9  d1 f10  d1 f11 d1 f12  d1 f13  d1 f14

Starting with f                 f1      f2       f3       f4        f5       f6       f7      f8        f9      f10      f11       f12      f13       f14    f14 d1

In Lanthanides starting with d1 and then f has 11 mismatches, whereas starting wifh f has 3 mismatches.

                                      Ac      Th     Pa      U       Np     Pu      Am     Cm     Bk,    Cf       Es       Fm      Md        No       Lr

Real                               d1      d2   d1 f2  d1 f3   d1 f4    f6       f7    f7 d1     f9      f10      f11       f12      f13       f14    f14 p1

Starting with d1 then f    d1   d1 f1  d1 f2  d1 f3  d1 f4  d1 f5  d1 f6  d1 f7  d1 f8  d1 f9  d1 f10  d1 f11 d1 f12  d1 f13  d1 f14

Starting with f                 f1      f2       f3       f4        f5       f6       f7      f8        f9      f10      f11       f12      f13       f14    f14 d1

In Actinides starting with d1 and then f has 10 mismatches, whereas starting wifh f has 7 mismatches.

I think it is clear which approach provides the better overall fit,

Mario RP

Virus-free.www.avast.com

[René]

On 27 Feb 2026, at 04:06, ERIC SCERRI <sce...@g.ucla.edu> wrote:

OK.  Let’s just agree to disagree.  

To me difference means either adding or subtracting!  

I think the move from V to Cr is therefore ambiguous regarding where the difference takes place since it is both in d and s orbitals.  

In any case why does this matter?

Upon reflection, it doesn’t matter, since ambiguous differentiating electrons (d/e) occur only within the d-block and don’t alter the overall predominance of d-type d/e in that part of the PT.

I suggest what does matter is this: if the predominant d/e informs block character, then the arrangement with fewer d/e anomalies—namely La-in-Group-3—is more congruent with that principle.

Per your commentary, the apparent difficulty is that, in the rarely displayed 32-column form, the La table produces a split d-block. However, 4f filling is well known to occur between 5d1 (La) and 5d2 (Hf), with 5d1 reappearing in Gd and Lu. The +3 ions progress smoothly from f1 in Ce to f14 in Lu. The visual interruption therefore reflects the actual filling sequence (d1 → f → d2–d10) rather than conceptual incoherence.

The issue is not perfection—neither the La nor the Lu form is flawless—but which arrangement better preserves the architectural logic from which block structure derives. On that criterion, the La-in-Group-3 PT is the preferred option. Principle and detail are better reconciled in this form.

cheers, René

[René]

On 27 Feb 2026, at 08:23, Mario Rodriguez <mavo...@yahoo.es> wrote:

Hi René,

I love travelling because it “forces” me to step away from duties and gives me unhurried time to think, something that’s rare in the life of a lecturer. Even though I’m sure we won’t convince each other on this topic, I’d like to share a few concise points.

Thanks Mario for sharing your thoughts about the Group 3 question.

In my responses I’ve tried to bear in mind three considerations

• a guiding philosophical principle
• the relevant details
• and the integration of the two.

To make the thread easier to follow by others I’ve added the following headings:

1. Th as an ideological Trojan horse
2. Ac (d¹) in the d-block; Th (d²) in the f-block
3. An arbitrary solution?
4. An f-block between d¹ and d²
5. Praise for the Madelung rule
6. Least mismatches with theoretical filling
7. Conclusion

1. Th as an ideological Trojan horse

Th can be seen as an "ideological Trojan horse" for Ac. If one accepts that Th (d²) can be placed in the f-block without having any electron in an f orbital, then the preceding logical element (d¹) can be placed there as well and, logically, must be.

While the preceding d¹ element—Ac—could also be placed in the f-block, there is no logical imperative for this to occur.

2. Ac (d¹) in the d-block; Th (d²) in the f-block

Your current classification of Ac (d¹) in the d-block and Th (d²) in the f-block is mainly because the element above Th, Ce, is not d², and including La, Ac, and Th altogether in the d-block would look awkward and aesthetically unappealing.

No, there’s no intrinsic requirement for the element above Th i.e. Ce to necessarily be d². Ce is in fact f¹d¹ making it, appropriately enough, the first element with an f-electron.

3. An arbitrary solution?

Hence, the solution becomes to declare, somewhat arbitrarily, that Ac (d¹) is d-block because it has a d electron, while Th (d²) is an “irregular” f-block element because it has d electrons.

The logical reasoning would be or both irregular in the f-block o both regular in the d-block.

While either of those two options sounds reasonable there’s no logical imperative necessitating one or the other.

Since Ac is the first element with a 6d differentiating electron, it could reasonably be expected to start the 6d row. Th, having two 6d electrons, may then also be expected to follow in that row, but the relevant position is already occupied by Rf. In the same way, there is no room for Lr in the p-block, despite its p differentiating electron, so it needs to be placed in either the d- or f-block.

I support Eric and Will Parsons in their foundational argument that, in choosing an optimal periodic table, the focus should be on the predominant differentiating electron (d/e) in any given block.

On that basis, a table with La–Ac in group 3 has one fewer d/e discrepancy than one with Lu–Lr in group 3.

Such a table also shows each block starting with the first appearance of the relevant d/e: s at H; p at B; d at Sc; and f at Ce. I see this pattern as logical and didactically helpful.

I suggest that Th, with its d type d/e, simply marks an irregular start to the 5f row, much as Lr marks an irregular start to the 6d row in an Lu table.

An La table further has the advantage of preserving double periodicity in both f-block rows. After the occurrence of a half-filled 4f subshell at Eu and Gd, the sequence repeats with the occurrence of a filled subshell at Yb and Lu. A similar, though weaker, periodicity appears in the actinides, with a half-filled 5f subshell at Am and Cm and a full subshell at No and Lr. This recurrence of half-filled and filled subshells reflects the underlying periodicity of electronic structure.

Placing Lu and Lr under Y obscures the start of the filling of the f-block (it would appear to start at La, a d-type element) and visually truncates its double periodicity (it would be cut off at Yb whereas it would actually end in the d-block).

4. An f-block between d¹ and d²?

I was also surprised when you said (I think to Larry) that it is “logical” for an f-block to lie between d¹ and d². There is, in fact, no f-block between Ac (d¹) and Th (d²).

I said to Larry that, on block-logic grounds, the 4f row lies between 5d¹ and 5d². So seeing d¹ → f → d²–d¹⁰ on the table feels natural. In this case, as mentioned, Th has an irregular differentiating electron.

5. Praise for the Madelung rule

At the same time, in your response to Eric, you praised the validity of the n + l rule. According to that rule, there is no d¹ stage between filling the s and f orbitals: the sequence is simply s → f → d.

Rather than praising the n + l rule I noted that its sequence alternated between being exact and anomalous (or irregular) and that after every irregularity or set of irregularities, the rule resumes working until the next irregularity or set of irregularities. It is like an aeroplane flying through turbulence and then returning to its intended flight path each time. Yes, according to the n + l approximation there is no d¹ stage between filling the s and f orbitals. In real life, however, there is, reflecting the well-known delayed onset of f-orbital filling.

6. Least mismatches with theoretical filling

What I meant by “The important feature is the overall fit should have the lowest mismatches with theoretical filling” refers to the table I already sent you, which has not been falsified yet…In Lanthanides starting with d1 and then f has 11 mismatches, whereas starting with f has 3 mismatches…In Actinides starting with d1 and then f has 10 mismatches, whereas starting with f has 7 mismatches.

I agree on this point; your table cannot be falsified. (Incidentally, this is the first time I have seen the table. I have no record of having previously received it from you.)

However, periodic table blocks are constructed on the basis of predominant d/e, rather than on the the exact match between electron counts and positions in a row.

On thorium more specifically, it is pertinent to note the f¹ configuration of the isolated gaseous Th³⁺ ion. Thus, while Th has an anomalous configuration, peeling away its outer electrons reveals a surprising outcome, more consistent with it being in the f-block.

When turning to the chemistry of the elements, condensed-phase configurations provide an additional perspective. A nice example is the configurations of the 4f³⁺ cations, which start at f¹ for Ce³⁺ and run through to f¹³ for Yb³⁺ and f¹⁴ for Lu³⁺. In this case there is a perfect match between the position number of the element in the 4f row and its number of f electrons. A near perfect match occurs for the 5f³⁺ cations of the actinides, Th to Lr. Here, +3 is the only state shared by all of the actinides, and for nine out of 14 of them is the most stable state. I say “near” perfect match since, in compounds—as opposed to the isolated gaseous form—trivalent thorium is routinely regarded as being d¹. The balance of energies between f¹ and d¹ is thus finely balanced.

7. Conclusion

I think it is clear which approach provides the better overall fit.

I agree. The multiple considerations listed above—block purity, block starts, double periodicity, periodic-table architecture, and condensed-phase configurations—seem to point in the same direction.

A similar observation applies to the divalent cations of the d-block elements. The number of d electrons in these ions corresponds to their position in the block. Trivalent cation configurations cannot be relied on here since there are no such species for the group 12 elements zinc, cadmium and mercury.

René