Right-Step PT

[Mark Leach]

Hi All,

Scott Hutchinson has sent me some excellent PT material over the last few years

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1225

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1228

And now he has sent me a comprehensive and beautifully produced PT document which I think will be of general interest to the group:

[ERIC SCERRI]

Thanks Mark,

I enclose a very brief response to the very first point in the Hutchinson PDF document you posted, concerning what he calls the forever group 3 wars, and which incidentally does not contain a single reference to the literature.  

I also include the article that I cited.

Perhaps I should also have added a point 3, namely disqualify the split d-block periodic table on the grounds of it’s ugliness and the fact that no other block is split, and certainly not in such an uneven fashion 

(For those of you who might claim that the s-block is split into two in the conventional form of the table).  

[ERIC SCERRI]

Dear Scott,

Apologies for butchering your name in my previous posting.

I blame our fearless leader, Mark Leach, for encouraging me to do so when he wrote 

Scott Hutchinson

Plus, people butcher my name all the time.  

It’s pronounced Scherri, not Skerri.

Eric

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<Right Step Periodic Table (RSPT) - response overview v3.pdf>

Mark Leach

meta-synthesis

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ERIC SCERRI

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

 

 

[Rene]

Thanks Eric.

Re point 3, aesthetic judgments are subjective, and what one viewer sees as ungainly, another may regard as an acceptable—or even appealing—reflection of underlying structure.

The s-block is commonly shown split into two on defensible physical and chemical grounds. Moreover, its 1:11 separation and the d-block’s 1:9 separation are in a comparable range of unevenness. Further, the split of the d-block is likewise based on physical and chemical grounds.

Whereas the "irregularity" of the split s-block is regularly seen, the split d-block is well hidden given the 32-column format is rarely used, owing to its inconvenient size and limited practicality for wall charts, textbooks, or teaching. In the much more common 18-column medium form, the f-block is footnoted, the d-block appears contiguous, and the visual objections largely disappear.

René

[johnmarks9]

First Chemical Canasta world championship kicks off in Harrogate, Yorkshire, England next month using this PT:

[ERIC SCERRI]

Dear Scott,

Can you please respond BRIEFLY the the following two questions?

1.  You claim that most periodic tables, including the traditional 18-column form, result in incorrect misalignments of elements.

It appears that you base this claim entirely on electronic configurations of atoms.

But why ignore completely the chemical similarities among the elements that are currently aligned in particular groups?

For example, Li, Na, K etc.

2.  Your proposed alignments are supposedly based on electronic configurations.  You even mention the work of Eugen Schwarz.  I can provide references if necessary.

Are you aware of the fact that for K and Ca, 4s electrons are the most energetic

and that for the first transition series, the same is true, since 3d orbitals are occupied BEFORE 4s, contrary to the Madelung rule?  This information has been discussed by Schwarz in several articles.

So even if we were to follow your suggestion and completely ignore all chemical similarities, there would still be a problem in attempts to base alignments according to the most energetic electron in each atom.

Regards

Eric Scerri

On Aug 12, 2025, at 7:28 AM, Mark Leach <ma...@meta-synthesis.com> wrote:

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<Right Step Periodic Table (RSPT) - response overview v3.pdf>

Mark Leach

meta-synthesis

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[Mario Rodriguez]

Hi René,

I have some observations regarding group 3.

I think that splitting d-block is not only a matter of ugliness. Although we know exceptions of Madelung rule, it's still taught that after filling 6s comes 4f and then 5d (same with 7s, 5f and 6d). There is no rule saying that after 6s, comes 5d1, then all 4f and then resumes to 5d2. In other words, the general rule is 6s1 to 6s2 to 4f1 to 4f14 to 5d1... Not 6s1 to 6s2 to 5d1 to 5d1 4f1 to 5d1 4f14 to 5d2...

And someone can reply that Lanthanum in the ground state has an electronic configuration of 5d1 6s2 and Actinium 6d1 7s2. And then I would reply that Praseodymium is 4f3 6s2 (as if the 2 previous elements were fully f as well), and Plutonium 5f6 7s2 (as if the 5 previous elements were fully f as well). Furthermore, Lutetium is 4f14 5d1 6s2 (starting the d block), and Lawrencium is 5f14 7s2 7p1 (although it fills a p orbital, the f orbital was filled in the previous element). There are more papers pointing out to inclusion of Lu and Lr to 3 group:

https://doi.org/10.1021/ed059p634 y https://doi.org/10.1007/s10698-015-9216-1 

https://doi.org/10.1080/00958972.2022.2084394

https://doi.org/10.1039/D3DT03738J

https://doi.org/10.1002/chem.202400131

Additionally, if Lanthanides and Actinides are f block, it makes sense that Lanthanum and Actinium, the elements that originate those names, are f block as well. Otherwise they should be called Cerianides and Thorianides.

It's also said that the excision of the current f block plus Lu and Lr from the rest of the current periodic table is a good solution to prevent this ugliness. However, rather than being a good solution, it creates confusion to students. Here a Reddit question of a confused student (there are many more): https://www.reddit.com/r/chemistry/comments/19azy8m/f_block_confusion_on_periodic_table/ 

The other point to justify the excision of the f block plus Lu and Lr is the current periodic table would be too long. I totally agree. To avoid confusing students with breaks while not having a too long representation, spirals may help. They also approaches halogens to alkali metals so hydrogen can contact both ;)

Mario RP

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[Scott Hutcheon]

1. This is the exact opposite of what is shown in the paper with the RSPT. Section 1 and Section 3. 

The Standard Periodic Table (SPT-18 and SPT-32) is near solely based on electronic configurations (forcing all s-periods into an s-block, forcing all d-periods into a d-block, forcing all f-periods into an f-block), except for duplet s2 Helium which is cobbled onto the octet p6 inert gases for bilateral symmetry and trying to conflate the duplet rule with the octet rule (which is also attempted with the 18-electron rule). The Left-Step (LSPT-32) is even more unscientific, by forcing H onto the Alkalis and He onto the Alkaline Earths simply for electron configurations (solely based on s-periods in an s-block, d-periods in a d-block, and f-periods as a separate f-block).

That is why the current iconic table contains obvious and known incorrect chemical relationships and similarities for ≈100% of all atoms in the universe and the Left-Step for 100% of all atoms in the universe (Hydrogen and Helium) simply for expediency as no solution was ever found or expected.

The RSPT instead maintains and continues all correct chemical groups and periodicities as they necessarily emerge from all known correct physical groups and periodicities (chemistry evolves from physics) by simply following basic orbital filling and atomic numbers (Z).

2. This is the exact opposite of the paper. The RSPT maintains and follows all known correct chemical and physical periodicities and similarities by ignoring the organizational compulsion of forcing periods into blocks based solely on their electronic configurations.

Per the paper: Section 1 — Figure 4d, Section 2 — Rules 1–4, Rule 8, Rule 10 (for orbital sharing and anomalies including Schwarz), Section 3 — Figures 18, 19, and 26b (Madelung).

Have reattached the latest version of the paper as it would be more efficient (and briefer) to respond to questions about particular Figures or Periodic Table Rules or Sections.

[Scott Hutcheon]

Hi Mario!

Per the attached paper, the RSPT follows both atomic numbering and orbitals to maintain all known current and correct physical and chemical similarities, periods, and relationships. With the CSPT and RSPT, the d-periods are not split up in the way you are imagining, but instead simply follow accepted orbital filling.

[ERIC SCERRI]

Thank you Scott,

I wonder if you could try to answer my specific questions?

Why do you ignore traditional chemical similarities among elements within a particular group?

Are you aware of the issues with the d-block metals, whereby the d orbitals are occupied preferentially, followed by the s orbitals?  Doesnt this interfere with what you say about “stacking” elements?

regards

Eric Scerri

<Right Step Periodic Table (RSPT) - response overview v4.pdf>

[Scott Hutcheon]

Yes, sorry if the answer was buried in the previous reply. See Section 2, Periodic Table Rule 10 of the paper, as well as Figures 19 and 26b–29b.

Otherwise there would be a lengthy copy-and-paste here with the same materials!

[ERIC SCERRI]

Hi Scott

How about you meet my question in a  direct way instead of directing me to one your rules?

Eric

On Aug 14, 2025, at 2:00 PM, Scott Hutcheon <scotth...@gmail.com> wrote:



[Scott Hutcheon]

No problem, though it won't be quite as clear:

The d- and f-periods should be placed so that anomalous ground state electron configurations (including those recently calculated by
German chemist W. H. Eugen Schwarz) are connected to the shared orbit periods:

The 3d-period anomalies (Cr, Fe, Co, Ni, Cu) share shells with the 4s-period;

The 4d-period anomalies (Nb, Mo, Tc, Ru, Rh, Pd, Ag) share shells with the 5s-period;
The 4f-period anomalies (La, Ce, Gd) share shells with the 5d-period;
The 5d-period anomalies (W, Os, Ir, Pt, Au) share shells with the 6s-period;
The 5f-period anomalies (Ac, Th, Po, U, Np, Pu, Cm) share shells with the 6d-period; and
The 6d-period anomaly (Lr) shares shells with the 7p-period.

The natural placement of the d- and f-periods further exposes the connected relationships between the sets of 4s-3d, 5s-4d, 6s-4f-5d, and 7s-5f-6d-7p period sequences. While the 3d-, 4d-, and 5d- period anomalies share shells with their earlier (previous) s-periods, and the 4f- and 5f-period share shells with their following d-periods, the 6d-period anomaly shares shells with the following 7p-period. The fact that the different 6d-period anomaly does not share a previous s-shell (unlike the other d-anomalies) cannot be ignored as a mere exception.

These period sequences required to maintain anomalous shell sharing require following basic orbital filling:

1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p → 8s → 5g → (...)

Reflected exactly in the corrected relative energy orbital filling chart:

7p →
6p → 7s → 5f → 6d → 
5p → 6s → 4f → 5d → 

4p → 5s → 4d →
3p → 4s → 3d → 

Which is simply flipped on its head (mirrored) for the RSPT:

3p → 4s → 3d →
4p → 5s → 4d →
5p → 6s → 4f → 5d → 
6p → 7s → 5f → 6d →
7p →

Again highlighting why 3d and 4d are naturally placed over 4f and 5f (revealing the Column of Instability and Natural Divide) and should not be artificially stacked as a solid block over 5d and 6d to satisfy normative theoretical beliefs while ignoring descriptive universal reality:

As it merely follows sequential atomic numbering and orbital filling (while naturally maintaining all correct chemical similarities, relationships, and periodicities) the RSPT can uncontroversially be understood as simply a flipped version of any corrected relative energy orbital filling chart.

[Rene]

Hi Scott

Thank you for sharing your work.

Here are four observations which I feel would make it difficult for the RSPT to gain traction among chemists or educators.

1. Breaking the Li-Na-K and Be-Mg verticals (per Eric). Separating Li from Na-K-Rb-Cs-Fr and Be from Mg-Ca-Sr-Ba-Ra disrupts the two most intuitive vertical relationships in the s-block:

• Shared valence electron configurations

• Recognisable chemical behaviour trends

This is a step away from the core achievement of the conventional PT: grouping elements vertically by their recurring chemical properties. It risks confusing learners who have just internalised these trends.

2. Lonesome H. As Eric suggested (2004), hydrogen is as subject to the periodic law as all the other elements are. The fact that it may not necessarily be placed in an unambiguous manner doesn't support its placement as a loner. The same applies to helium.

Scerri E 2004, The placement of hydrogen in the periodic table, Chemistry International, vol. 26, no. 3, https://publications.iupac.org/ci/2004/2603/ud2_scerri.html

3. Mixing transition and f-block metals in a group. When ten “groups” each contain two transition metals and two f-block metals, the differences overwhelm the similarities:

• Electronic structure: d-block vs f-block behaviour is largely distinct.

• Chemistry: oxidation state ranges, coordination tendencies, and ionic radii behaviour diverge significantly.

• History and usage: f-block chemistry is typically taught as a specialised topic, so its juxtaposition with mainstream transition metals seems arbitrary.

The result is that the "group" label risks becoming nominal only, without a coherent chemical identity.

4. Your claim that "reality is entirely asymmetric". Reality blends symmetry and asymmetry, so if bilateral symmetry in a periodic table reflects genuine periodic trends rather than distorting them, it is clarifying, not contrived. Please see the attached example.

René

Capstone step pyramid periodic table. Four kinds of bilateral symmetry are evident: its shape; four block types in each half; metals and nonmetals in each half; and a subatomic particle in each half.    

[Jess Tauber]

I just want to add to Rene's Point 4. Symmetry exists all the way up from subatomic particle physics to biochemistry, not to mention abiological chemistry. And though perhaps harder to see, perhaps into cosmology as well. Same for asymmetry. And don't forget antisymmetry thrown in for good measure. Symmetry is even found in human languages, artistic creations, logic and mathematics.

Jess Tauber

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[Scott Hutcheon]

Regarding symmetry and asymmetry: we must always guard ourselves (a continuing point in the RSPT paper) between how the universe is and how we want it to be. There is indeed theoretical symmetry, but there is no symmetry in reality (mathematical symmetry regarding orientation is not the same thing).

There is theoretical symmetry in baryons (matter and antimatter), but there is no baryon symmetry in reality (or there would be no universe and no Physics and certainly no elements and therefore no Chemistry and no Biology and no periodic tables). There is theoretical symmetry for time, but there is no symmetry for time in reality (or there would be no Physics, no universe, and no Chemistry -- as asymmetrical time is required for nuclei formation and electron cloud orbitals around nuclei and asymmetrical time is required for chemical reactions, etc. -- and no Biology and no periodic tables. There is therefore no symmetry for elements and any periodic table showing any non-mathematical-orientation-symmetry is simply an often beautiful (bilaterally symmetric) purely theoretical model. 

Recent understandings can be searched and studied to clarify just how many asymmetries there are at every level of science and reality.

As per the RSPT overview paper, there is also no symmetry in handedness at the basic informational level or up through the subatomic particle physics or in chemistry or biochemistry or biology (human right handedness for example). Review the horrors of trying to force symmetry even onto just handedness within macro-level biological molecular chirality because of theoretical beliefs and misunderstandings slamming into reality (Thalidomide).

For the exact same reasons above, bilateral symmetry is of course possible in human theoretical (including religious and philosophical and psychological) periodic tables, it's just not possible for any periodic tables based in universal reality.

As we all know, the step-pyramid periodic table is a bilaterally near symmetrical attractive artificial construct that has been rehashed since at least its invention in 1882 by Bayley (true science is built on discoveries that lead to falsifiable theories not beliefs that lead to unfalsifiable invented works of art):

Sidenote: it really is a shame that William Jensen passed (2024) before the CSPT and RSPT could be shared with him, even though he probably would have hated it.

The RSPT paper already clarifies the issues with the anti-scientific (versus the Copernican Principle) local human-centric fitness and beauty desires of bilateral symmetry. It also arms us with basic initial tools (the Periodic Table Rules) to help recognize artificial constructs, which will be used again here regarding the capstone step-pyramid scheme periodic table:

1. Per the paper, like most artificial tables, this very imaginative form (which obviously required an admirable amount of creative work) attempts to force the joining of s- and d-periods into solid neat and tidy visually pleasing organizational blocks to satisfy the same theoretical belief we've seen again and again regardless of natural universal reality (orbital filling where  1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p → 8s → 5g → means that stacking the d-periods into a d-block ignores f-period displacement of the later transition d-periods, and requires mental gymnastics and convoluted fictive visual creations to include such stacking). 

While it wasn't mentioned before, the g-periods would also displace the f-periods which would further displace the d-periods and further verify the artificiality of stacking d-periods into a d-block (whereas there are uncontroversially no issues for the p-periods block and 3+ s-periods block):

3p → 4s → 3d →
4p → 5s → 4d →
5p → 6s → 4f → 5d → 
6p → 7s → 5f → 6d →

7p → 8s → 5g → 6f → 7d →

8p → 9s → 6g → 7f → 7d →

This cannot be hand waved away as "we won't discover those elements" -- to again ignore the Copernican Principle where we seem to have forgotten the basic principles of science that have made it so successful and have begun to allow normative (religious, philosophical, psychological) belief-based theories to drift back in and hijack the scientific program and directive over uncovering reality as it actually is and not just how we normatively want it to be.

2. Per the paper, this form claims the electron (e) and the Neutron (N) as Period 0, despite any 0s or Period 0 being the Free Proton and Alpha Particle based on the universal reality of Chemistry (starting at 1s) evolving from Physics.

3. Stacking Hydrogen primarily over the traditional Group 1 Alkali Metals and secondarily over the traditional Group 17 Halogens ignores physical and chemical reality for 92% of the atoms in the universe. Meaning the table is already (without considering the Free Proton and Alpha Particle proportionality mistakes) generously only 8% correct for universal reality.

4. Per the paper, stacking s2 duplet Helium primarily over the p6 octet traditional Group 18 Inert gases and secondarily over the Group 2 Alkaline Earths means the table is now another ≈8% incorrect for the atoms in the universe and their physical and chemical relationships. The capstone  is more than 100% incorrect for universal reality within the first two rows.

5a. While visually Period 1 starts off strong (symmetric blocks and relationships to Period 2), there is little actual symmetry for the rest of the table (other than gross general visual symmetry) when, for example, Period 2 has two s-blocks and two p-blocks on one side yet four p-blocks on the other, and completely unequal primary and secondary relationships. 

5b. Placing H (one electron and one proton) which makes up 92% of all atoms and 74% of all mass, as visually related or equivalent to He (two electrons and the two proton and two neutron, along with the three-body problem, etc.) which is ≈8% of all atoms and 24% of all mass sticks purely and solely to the physical electronic configurations of elements (ignoring nature for theories) -- even without considering their exponentially different chemical properties and ignoring the potential Mass 2 and 3 pre or proto-roadblocks between H and He.

5c. Per the paper, the capstone cannot visually address the reality of elemental evolution and the Mass 5- and 8-Roadblocks before 2s duplet Li and Be.
 

5d. Rather than further going into gruelling detail pointing out how forcing bilateral symmetry onto a periodic table can only reinforce a biologically pleasing yet physically shallow understanding of true symmetry, it might be better to show here how little actual symmetry there is between periods, blocks, primary, and secondary (dotted line) relationships (a picture speaks a thousand words and all that):

5e. Per the paper, using Periods 1–7 obscures and should be replaced by the orbital periods, as even the main contender Left-Step has Periods 1–8 and different orbitals within each Period. The Group numbering system is also an incorrect historical legacy (skipping the f-periods) that is better reset and updated.

6. The current Standard Periodic Table (SPT-18) was a paradigm shift (even despite the f-periods being banished and basically ignored upon their discovery), after which the theoretical as well as experimental and observational research experts found physical and chemical relationships to reinforce the form (many beyond those that are real). The same thing happened with Mendeleev and the other 8-column tables, and with the other 18-column tables, and the other 32-column tables. The same thing continues to happen with the Forever Wars over Group 3 content and Hydrogen and Helium placements.

We will always a-historically forget just how many dead-ends and mistakes were created and assumed around current and potential (expected or predicted) physical and chemical relationships (often for decades) before the next truer and more fundamental paradigm shift started the process again (evolution of science).

Per the paper, human nature guarantees that artificial tables will lead to artificial physical and chemical relationships being created and then defended by their creators (https://en.wikipedia.org/wiki/Apophenia). 

If at least the CSPT (placed in any textbook front endpage), if not the RSPT (placed in any textbook back endpage during a, ahem, transition period), is utilized, there will soon be more correct chemical and physical relationships found (often through attempts to disprove) between the correctly organized d- and f-periods (beyond even the critical REE elements aka the Earth Metal MEDIATES (Figure 4d) that help sustain the Scylur-Scylac Skirmish).

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[Scott Hutcheon]

Just in case anyone hasn't seen the brief article published over three years ago right after the original discovery (you don't have to be a member of LinkedIn to view): 

https://www.linkedin.com/pulse/possibly-last-periodic-table-youll-ever-need-scott-hutcheon/

It contains animations that show how the CSPT and RSPT are only correcting tweaks to the Standard and Left-Step Tables (maintaining all correct periods and blocks and their related physical and chemical similarities and relationships), which may relieve skeptics expecting that the tiny corrections based on reality were instead some sort of esoteric theoretical or artistic reimagining .

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[Jess Tauber]

In linguistics, we recognize clause structures as exhibiting symmetry patterns. A head is a higher node in a branching tree structure representing a phrase or the clause under which the phrase is contained hierarchically. A verb-initial phrase, as in Mayan languages, is said to be left-handed, because the verb comes first before syntactically dependent structures, such as noin phrases. The verb is the hierarchical head of the verb phrase. In languages like Japanese, on the other hand, the verb tends to come at the end of the clause, so we call Japanese right-handed. All sentence structures in any one language tend to follow the same head-dependent ordering pattern, unless they are marked for some other function. Prosody and syllable structures also tend strongly to favor one pattern versus another, to make processing easier on the brain. In English rhyme is much more common than alliteration, but in Khmer it's the other way around.

[Scott Hutcheon]

Hi Jess!

Sorry, might be burying the lead again. The Scientific Method (particularly with the generalized Copernican Principle) requires that scientific truths be universal and not based solely on our local human experience. With Astronomy (and some Cosmology theoretical support) we know that Physics (including element formation) and Chemistry (including element interaction) are the same throughout the universe which means a scientific periodic table would be required to visually reinforce the known physical and chemical similarities, properties, and periodicities that apply everywhere.

Per the RSPT paper, for the current standard periodic table and almost every other variant the focus on local artificial bilateral symmetry (due to human normative genetic and epigenetic beliefs and desires around fitness and beauty) and the focus on artificially stacking (of all s-periods in one s-block, d-periods in one d-block, and f-periods in one f-block) due to local human normative theoretical desires and beliefs (religious, philosophical, and psychological) around completionist and organizationalist theories (n+l rule forced onto chemical periodicity as well as the forced conflation of the duplet rule, octet rule, and 18-electron rule) which are against natural reality (physical orbital filling from which chemical properties and periodicities emerge/arise) mean that such tables cannot be scientific as they give incorrect relationships for ≈100% of atoms in the universe and are therefore ≈0% scientific.

Similarly, yes, local human experience may find that language clause structures appear perfectly symmetric but we have no way of knowing if sentient beings throughout the universe use the same symmetric clause structures in their languages (or even if they have languages), which means it is unfalsifiable and unverifiable and therefore unscientific as a universal rule. Also, it would only be a local scientific fact if every known human language contained the same type of symmetric clause structures. Otherwise, it would then be a scientific fact only for each specific language that contains symmetric clause structures.

The Standard Periodic Table and the Left-Step (and most other variants) don't even work locally (still ≈100% wrong for our solar system) but were originally (due to knowledge 153 up to 80 years ago) incredible breakthrough monumental discoveries designed for local human use (lab work, research, etc.) and expediency (due to at least a lack of consensus over Group 3 content and Hydrogen/Helium placement) -- and because no actual scientific solution had be found after thousands (if not tens of thousands) of attempts we have have settled upon and ingrained and continue teaching children and future scientists to venerate a known to be ≈100% wrong periodic table (and then even double down and claim it as an iconic exemplar of science).

Also, at a deeper level, when looked at closely enough, nothing can actually be perfectly symmetrical in reality (despite our wishes and theories making it seem possible) just as there are no straight lines in reality (which is why we must use non-Euclidean mathematics to model reality).

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[Rene]

On 16 Aug 2025, at 07:46, Scott Hutcheon <scotth...@gmail.com> wrote:

Regarding symmetry and asymmetry: we must always guard ourselves (a continuing point in the RSPT paper) between how the universe is and how we want it to be…

Scott

It seems we’re talking past each other a little. I don’t deny the reality of asymmetries—they’re crucial in physics and chemistry. My point is that symmetry and asymmetry coexist: laws often express symmetries, while their manifestations often break them in structured ways.

A periodic table that incorporates bilateral symmetry isn’t automatically a denial of asymmetry; it can be a visual way to highlight repeating regularities that do exist in quantum numbers, model-based electron configurations, and chemical trends. The question is not whether symmetry is “artificial” but whether the table illuminates or obscures the periodic law.

One of the simplest bilateral patterns in the periodic table is the relationship between metals and nonmetals. The distribution is certainly uneven, but the pairing is still evident—as are the parallels between the noble metals and noble gases, and between the alkali metals and halogen nonmetals. The RSPT, however, makes these bilateral relationships harder to discern, for example by placing the noble metals in two separate regions.

I’d also note that the conventional periodic table is designed to reflect the chemistry of elements under ambient to near-ambient conditions, which is why Li sits naturally over Na, and Be over Mg. While hydrogen’s cosmic abundance is important in astrophysics, it isn't the primary organising principle for a chemical table. The periodic law is about recurring physical and chemical properties, not cosmological proportions.

René

[Scott Hutcheon]

Hey René, appreciate the feedback,

Yes, we're probably talking past each other (and it's probably on me). Totally agree with repeating quantum number, electron configuration, and chemical trend regularities and periodicities, would argue that they are not symmetrical in any way (per natural orbital filling chart versus theories) and that forcing them into artificial stacked blocks and/or bilateral symmetry form reduces their connection to universal reality in favour of local use (which I think you're arguing as a feature in the last two paragraphs)! 

As in the paper, have argued that forcing bilateral symmetry, as none actually exists, obscures relationships (example, when dropping the f-periods for the standard table) rather than clarify them.

Had definitely considered how adversely working chemists would react to a periodic table based on elemental evolution and its discovered direct connection to sequential atomic numbers and physical periodic orbital filling (which is the fundamental reason for chemical properties, similarities, and periodicities), and had created the RSPT – Chemistry Lab variant in the first round of creation three years ago. 

As the RSPT is based on basic physical reality, it was a simple solution, and the row spaces between H and the Halogens and He and the inert gases do visually indicate/reinforce just how physically different and chemically unrelated they are though:

However, per the paper, would again argue that placing simpler duplet s2 Helium over the much more complex octet p6 inert gases signals apophenia (https://en.wikipedia.org/wiki/Apophenia) or judicially choosing (cherry picking) data points, while ignoring counterpoints, to support a pet theory (that the duplet rule and 18-electron rule match the octet rule, which is what they were invented to do). 

While the octet rule continues to be widely taught, the duplet rule not so much for good reason, and the 18-electron rule has so many exceptions as to not even be a rule. Would also disagree with Hydrogen over the Halogens as another example of seek and ye shall find relationships.

Had even created a version showing (like the updated capstone you shared) the  RSPT – Chemistry Lab variant including the (correct here!) 0s or Period 0 pre- or proto-elements:

Would these versions work better towards addressing your concerns for local human working chemists?

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[Rene]

Hi Scott

Glad to provide some feedback.

I haven't read your 38-page pdf since, ostensibly, the RSPT by itself appeared replete with problems.

Yes, the conventional periodic table is based on the periodic law in ambient to near ambient conditions rather then any purported connection with universal reality.

In terms of the smoothness of physical and chemical property trends going down each group, H over F is a rather good fit. And He over Ne is an optimal fit. There's no need to, as you say, seek and find such relationships; the numbers speak for themselves. There is further no need to float H and He above F and Ne. It is well understood that H isn't a halogen, even when positioned directly above F, and that He is s2 whereas the other noble gases are s2p6, even when He is positioned directly above Ne.

Can you address my observation about the noble metals being spread across two regions in the RSPT, as well as the mixing, across ten groups, of two transition metals and two f-block metals in each group?

Also of concern is the separation of the third row transition metals (Lu to Hg) from their second row counterparts (Y to Cd). This is an issue since a hallmark of transition metal chemistry is the similarity of most of the third row transition metals to their second row counterparts.

René

On 17 Aug 2025, at 11:34, Scott Hutcheon <scotth...@gmail.com> wrote:

Hey René, appreciate the feedback,

Yes, we're probably talking past each other (and it's probably on me). Totally agree with repeating quantum number, electron configuration, and chemical trend regularities and periodicities, would argue that they are not symmetrical in any way (per natural orbital filling chart versus theories) and that forcing them into artificial stacked blocks and/or bilateral symmetry form reduces their connection to universal reality in favour of local use (which I think you're arguing as a feature in the last two paragraphs)! 

As in the paper, have argued that forcing bilateral symmetry, as none actually exists, obscures relationships (example, when dropping the f-periods for the standard table) rather than clarify them.

Had definitely considered how adversely working chemists would react to a periodic table based on elemental evolution and its discovered direct connection to sequential atomic numbers and physical periodic orbital filling (which is the fundamental reason for chemical properties, similarities, and periodicities), and had created the RSPT – Chemistry Lab variant in the first round of creation three years ago. 

As the RSPT is based on basic physical reality, it was a simple solution, and the row spaces between H and the Halogens and He and the inert gases do visually indicate/reinforce just how physically different and chemically unrelated they are though:

<RSPT-36 - schwarz full colour -chemistry model.png>

However, per the paper, would again argue that placing simpler duplet s2 Helium over the much more complex octet p6 inert gases signals apophenia (https://en.wikipedia.org/wiki/Apophenia) or judicially choosing (cherry picking) data points, while ignoring counterpoints, to support a pet theory (that the duplet rule and 18-electron rule match the octet rule, which is what they were invented to do). 

While the octet rule continues to be widely taught, the duplet rule not so much for good reason, and the 18-electron rule has so many exceptions as to not even be a rule. Would also disagree with Hydrogen over the Halogens as another example of seek and ye shall find relationships.

Had even created a version showing (like the updated capstone you shared) the  RSPT – Chemistry Lab variant including the (correct here!) 0s or Period 0 pre- or proto-elements:

<RSPT-36 - schwarz full colour -chemistry model - 0s.png>

Would these versions work better towards addressing your concerns for local human working chemists?

Virus-free.www.avast.com

On Sat, Aug 16, 2025 at 6:39 PM Rene <re...@iinet.net.au> wrote:

On 16 Aug 2025, at 07:46, Scott Hutcheon <scotth...@gmail.com> wrote:

Regarding symmetry and asymmetry: we must always guard ourselves (a continuing point in the RSPT paper) between how the universe is and how we want it to be…

Scott

It seems we’re talking past each other a little. I don’t deny the reality of asymmetries—they’re crucial in physics and chemistry. My point is that symmetry and asymmetry coexist: laws often express symmetries, while their manifestations often break them in structured ways.

A periodic table that incorporates bilateral symmetry isn’t automatically a denial of asymmetry; it can be a visual way to highlight repeating regularities that do exist in quantum numbers, model-based electron configurations, and chemical trends. The question is not whether symmetry is “artificial” but whether the table illuminates or obscures the periodic law.

One of the simplest bilateral patterns in the periodic table is the relationship between metals and nonmetals. The distribution is certainly uneven, but the pairing is still evident—as are the parallels between the noble metals and noble gases, and between the alkali metals and halogen nonmetals. The RSPT, however, makes these bilateral relationships harder to discern, for example by placing the noble metals in two separate regions.

I’d also note that the conventional periodic table is designed to reflect the chemistry of elements under ambient to near-ambient conditions, which is why Li sits naturally over Na, and Be over Mg. While hydrogen’s cosmic abundance is important in astrophysics, it isn't the primary organising principle for a chemical table. The periodic law is about recurring physical and chemical properties, not cosmological proportions.

René

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[Jess Tauber]

Symmetry in orbital filling. All orbital rows have even numbers of member elements, and it has been demonstrated that so far as orbital 'lobes' are concerned (except for s, where there is only one, so it is not termed a lobe for some reason), all lobes fill SINGLY with electrons with the orbital rows from left to right (regardless of WHAT that lobe represents in terms of f, d, p, or s) and then only after all lobes are filled with single electrons, does the system allow for second electrons to fill the lobes, with opposite spin, again from left to right. It is only this that allowed me to discern that atomic numbers that are also Fibonacci numbers all have either only first single or first doubled electrons filling lobes, and this depending on whether the Fib atomic number was odd or even- Fibonacci numbers come in groups of three, of which the first two are odd, and the third even, so (1,1,2)(3,5,8)(13,21,34)(55,89,144).... 

 Related Lucas numbers have the opposite pattern of (even, odd, odd), so (2,1,3)(4,7,11)(18,29,47)(76,123,199)..... Curiously, the Lucas numbers also exhibit, as atomic numbers, the reverse orbital filling trend to Fib atomic numbers, albeit less faithfully. The trend has LAST single or doubled electrons in lobes within orbital rows, again depending on whether the atomic number is odd or even.  The Fib pattern holds perfectly up to atomic number 89, but is off track re predicted orbital structure for 144. The Lucas trend gets off track starting with 29. However, the Lucas trend has FIXES that bring later atomic numbers at least partially into line with the trend, based on internal electron shifts between orbitals (29 and 47, 'coinage' metals copper and silver, respectively, and interestingly in the same group, both have atheoretical d9 structure, but in reality have shifted an s-electron to said d-orbital, thus filling it anyway despite its mispositioning in the idealized table. In the case of 76, osmium, the element behaves somewhat like a noble gas (all of which occupy final even positions within their orbital rows, all with doubled electrons), with severely reduced reactivity in the monatomic gaseous state. The trend goes off track completely after this point, so that atomic Lucas number 123 (not yet, if ever, synthesized) being completely mispositioned in the table.

The symmetries here are imperfectly realized/instantiated, but they ARE there.

Jess Tauber

tetrahed...@gmail.com

[Scott Hutcheon]

Hi Jess,

S-orbitals have a spherical shape: therefore they do not have lobes because the probability of finding the electron is the same in all directions from the nucleus.

1s (2) → 2s (2) → 2p (6) → 3s (2) → 3p (6) → 4s (2) → 3d (10) → 4p (6) → 5s (2) → 4d (10) → 5p (6) → 6s (2) → 4f (14) → 5d (10) → 6p (6) → 7s (2) → 5f (14) → 6d (10) → 7p (6) →

I honestly get that because each orbital period contains an even number of elements there is an incredible temptation to satisfy our very strong human desires to force bilateral symmetry. A great deal of creative work went into artificially organizing the current standard periodic table to appear nearly bilaterally symmetrical and balanced despite having an uneven 7 s-periods connected to an even 6 p-periods, an even 4 d-periods, and an even 2 f-periods.

However, exactly as you say, each orbitals fills "up" spin sequentially "left to right" before then filling "down" spin sequentially "left to right" per Pauli's exclusion (though why the left to right "up" spin first hasn't been adequately explained from first principles). This means the only possible electronically symmetric elements in each orbital period are the end ones (even number of all up and all down spins filled). This is also why the symmetrically filled octet gases are so stable. 

Symmetric = stable is a good way of looking at it (so every atomic, and therefore electronic, even-numbered element is more stable up to the most stable fully symmetric ones at the end of each period). This is exactly why the periodic table cannot be symmetric -- as only the final elements in each period are electronically symmetrical. Which is only 19 elements out of the 118 (an uneven number due to the uneven 7 s-periods). 

This is why the "final" end even-numbered elements of 5d and 6d (only realized with the RSPT) are liquid at standard (unlike 3d and 4d which are not, which is a further reason they shouldn't be stacked together). It's also why period end even-numbered elements form gases at 1s2 and p6, why the Column of Instability is at uneven lobes 5, and why the column of anomalous configurations is at even lobes 8, etc. 

But a deeper, more comprehensive understanding than symmetry and even-numbered stability needs to be discovered to understand why the rest of the s2 elements aren't as stable on their own (or have unique shared characteristics like the p6 gases), why 1s1 Hydrogen is a gas, other related issues with the p-elements, and the same for the 3d and 4d and 4f and 5f period end even and symmetric elements.

This symmetry related to even-numberedness also exists for the nuclei with magic and doubly magic symmetrically stable and even-numbered protons (and neutrons including for isotopes).

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[Scott Hutcheon]

Can you address my observation about the noble metals being spread across two regions in the RSPT, as well as the mixing, across ten groups, of two transition metals and two f-block metals in each group? Also of concern is the separation of the third row transition metals (Lu to Hg) from their second row counterparts (Y to Cd). This is an issue since a hallmark of transition metal chemistry is the similarity of most of the third row transition metals to their second row counterparts.

This is answered in the RSPT paper with Figures 7a, 7b, 7c, and 7d where electron affinity, electronegativity, ionization energy, atomic weight, and orbital-filling trends expect the corrected d- and f-period configurations. 

Also, they are termed early and later transitional metals because 5d- and 6d- come after (are displaced by) the f-periods -- as orbital filling and anomalous configuration shell sharing requires any scientific periodic table to sequentially follow:

4s→ 3d→ 4p→ 5s→ 4d→ 5p→ 6s→ 4f→ 5d→ 6p→ 7s→ 5f → 6d→ 7p→

We can't add artificial gaps between periods to create artificial stacks of periods to satisfy theoretical beliefs.

Per the paper, though it isn't satisfying because we want the universe to be a certain way, regardless of the artificial shared chemical properties we find within an artificial table, those artificialities (here stretched or distant similarities found between synthetically stacked 4d and 5d forced counterparts) would fall before and give way to more straightforward shared chemical properties after properly configuring periods and group columns (based on orbital filling). If the 3d and 6d forced counterparts (in the artificially stacked d-periods) also exhibited such a close spectrum of the same similarities, then it would be a different case.

Also, some similar characteristics are naturally expected of different d-periods with the same electron-filled "lobes" (at different levels) but that does not allow for the basic physical orbital filing order (from which all these chemical characteristics fundamentally arise) to be ignored.

Oppositely, we all accept, and so do both the standard periodic table and the RSPT (due to the same orbital filling that requires the d- and f-periods correction) that the p-periods are naturally stacked as a p-block despite the fact that they are a mixture of reactive nonmetals, metalloids, and other metals with a wide range of differing characteristics. There is no controversy in this (due to the same orbital filling) though there is no satisfying fundamental unifying explanation for it either. 

Per Figures 31a and 31b, the RSPT also more clearly follows metallicity trends (and all other trends) without the convoluted paths of the current standard table and with fewer exceptions -- especially if using the recently shared Chemical Lab variant where the left arrow would be pointing straighter up through the reactive nonmetals towards the Chemical Lab variant placement of Helium and Hydrogen.

The RSPT simply exactly follows periodic physical orbital filing from which all periodic chemical similarities arise.

I've attached an expanded and updated v5 of the RSPT overview paper -- thanks to discussions and feedback! The paper is quite different from what it might be guessed to be, and it's difficult/repetitive to respond/discuss if it hasn't been understood or presupposed (it's a quick read with many graphics).

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[ERIC SCERRI]

On Aug 17, 2025, at 8:49 PM, Scott Hutcheon <scotth...@gmail.com> wrote:

Hi Jess,

S-orbitals have a spherical shape: therefore they do not have lobes because the probability of finding the electron is the same in all directions from the nucleus.

1s (2) → 2s (2) → 2p (6) → 3s (2) → 3p (6) → 4s (2) → 3d (10) → 4p (6) → 5s (2) → 4d (10) → 5p (6) → 6s (2) → 4f (14) → 5d (10) → 6p (6) → 7s (2) → 5f (14) → 6d (10) → 7p (6) →

I honestly get that because each orbital period contains an even number of elements there is an incredible temptation to satisfy our very strong human desires to force bilateral symmetry. A great deal of creative work went into artificially organizing the current standard periodic table to appear nearly bilaterally symmetrical and balanced despite having an uneven 7 s-periods connected to an even 6 p-periods, an even 4 d-periods, and an even 2 f-periods.

Dear Scott,

I would be curious to hear of any evidence for this view.  Please cite at least one published paper in which the authors claim to be trying to achieve some kind of bilateral symmetry in their periodic table.

I just don’t believe that anybody has seriously attempted to do this.

It’s also very naive to think that we are necessarily dealing with 7 periods

However, exactly as you say, each orbitals fills "up" spin sequentially "left to right" before then filling "down" spin sequentially "left to right" per Pauli's exclusion (though why the left to right "up" spin first hasn't been adequately explained from first principles).

This is just a matter of convention.  Nobody who actually works in the field believes that spin up fills first.

The Pauli Principle is associated with the indistinguishability of electrons.

So to claim that a particular electron has up rather than down spin and that up spin is preferentially occupied is nonsense.  There is nothing to explain.  Its a convention.  The first electron has a 50% probability of actually having

a down spin to borrow your way of thinking.

Given that you have published absolutely nothing on this subject, would it not be an idea to express a little more humility, rather than trying to convince folks here of the way things really are?

This means the only possible electronically symmetric elements in each orbital period are the end ones (even number of all up and all down spins filled). This is also why the symmetrically filled octet gases are so stable. 

Symmetric = stable is a good way of looking at it (so every atomic, and therefore electronic, even-numbered element is more stable up to the most stable fully symmetric ones at the end of each period). This is exactly why the periodic table cannot be symmetric -- as only the final elements in each period are electronically symmetrical. Which is only 19 elements out of the 118 (an uneven number due to the uneven 7 s-periods). 

This is why the "final" end even-numbered elements of 5d and 6d (only realized with the RSPT) are liquid at standard (unlike 3d and 4d which are not, which is a further reason they shouldn't be stacked together). It's also why period end even-numbered elements form gases at 1s2 and p6, why the Column of Instability is at uneven lobes 5, and why the column of anomalous configurations is at even lobes 8, etc. 

But a deeper, more comprehensive understanding than symmetry and even-numbered stability needs to be discovered to understand why the rest of the s2 elements aren't as stable on their own (or have unique shared characteristics like the p6 gases), why 1s1 Hydrogen is a gas, other related issues with the p-elements, and the same for the 3d and 4d and 4f and 5f period end even and symmetric elements.

This symmetry related to even-numberedness also exists for the nuclei with magic and doubly magic symmetrically stable and even-numbered protons (and neutrons including for isotopes).

There is a good reason for this.  Shells consist of groups of orbitals and electrons go into orbitals two by two.

To achieve a full shell, regardless of whether one is dealing with electrons or nucleons, necessarily involves an even number of these particles (multiples of 2).  Again, there is no mystery here, for anybody who has actually studied and understood a little chemistry and physics.

I also agree with Jess Tauber’s general statement that symmetry lies at the heart of all of this.

If you are interested in pursuing this line of thought, it’s called "group theory".  There are many articles relating to the role of group theory as a means to understand the periodic table.  

This is another reason why a knowledge of the literature, and what has gone before, is an essential prelude to attempts to pontificate to others in this or any other forum.

Eric Scerri

To view this discussion visit https://groups.google.com/d/msgid/PT-L/CANbBqwiaH%2BW2KX36GSW9SY7PefSQNJt1MH3sMD4m%2BO4HRetaJg%40mail.gmail.com.

[Jess Tauber]

Note that although doubly-magic nuclei are the most stable, and tend strongly to be spherical, the sphericity is an APPROXIMATION, as the nuclei themselves consist of nucleons, thus the nucleus would seem 'pebbled' on its surface (the way a blackberry fruit does), The overall symmetry veers towards sphericity, while most of the less stable nuclides exhibit shapes approximating deformed ellipsoids (most of which are prolate, with the minority oblate). An even smaller minority have decidedly odd shapes, with things like single nucleons orbiting the main nucleus at some small distance from it.

There is also a link between the electronic and nuclear shell systems, despite differing emphases on constructional primitives. Whereas the LST has every period length occurring twice (each length being a half square of an even integer, or twice square of an odd integer), so that each pair of same-length periods in the LST consists of a square of even integer number of elements (4 for 1 and 2s, 16 for 2p3s and 3p4s, 36 for 3d4p5s and 4d5p6s, and 64 for 4f5d6p7s and 5f6d7p8s (if we ever manage to synthesize elements 119 and 120), each LS-motif nuclear shell (disregarding intruders) has only ONE shell of any particular length, and each of these lengths is a doubled triangular number (from the Pascal Triangle). The shells have a different constructional prioritization from electronic shells. In the latter, orbital parity alternates for any period that has more than one. S is positive, p negative, d positive again, and f negative. In the simple harmonic oscillator nuclear shell system all shells consist of 'orbitals' of the SAME parity. 

The magic numbers terminating each shell here are all doubled tetrahedral numbers from the Pascal Triangle. In Pascal Triangle combinatorics tetrahedral numbes are running sums of triangular numbers, and triangular numbers are running sums of integers (1, 1+2=3, 1+2+3=6, 1+2+3+4=10, etc.). The doubled tetrahedral magic numbers ending nuclear LS (harmonic oscillator) shells are TWICE the length of every other LS electronic period terminal (s2) atomic number.

In both systems there are EIGHT shells- for the electronic 4 sets of TWO same length LS periods, and for the nuclear 8 single LS shells. The math all fits nicely. 

Jess Tauber

To view this discussion visit https://groups.google.com/d/msgid/PT-L/8B2BCE68-1B76-4873-A211-7EC10D875434%40g.ucla.edu.

[Scott Hutcheon]

Hello all,

As the discussion seems to have gone away from the contents of the RSPT paper, let's reset and focus. 

Since the paper bypasses all current and previous well-worn and memorized judicial theoretical arguments by returning to the basic natural reality of physical and chemical orbital periods and their properties, similarities, and periodicities, it should be made clear here that it is obvious to anyone who has read the paper that responses instead coming from assumed understandings or preconceived notions about the RSPT or the paper will not hold up or even be relevant after reading the paper.

Based on René's preference for the Chemistry Lab RSPT-32 variant (which contains the same basic scientific objective truth value as the RSPT-36, if not more in some cases), I've added such variants where relevant in the paper!

Please respond to or raise issues with the attached v6 paper. For anyone who has read earlier versions, only the last few pages of Section 1 and Section 3 have been updated and expanded.

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[ERIC SCERRI]

On Aug 19, 2025, at 2:54 PM, Scott Hutcheon <scotth...@gmail.com> wrote:



Hello all,

As the discussion seems to have gone away from the contents of the RSPT paper, let's reset and focus. 

Since the paper bypasses all current and previous well-worn and memorized judicial theoretical arguments by returning to the basic natural reality of physical and chemical orbital periods and their properties, similarities, and periodicities, it should be made clear here that it is obvious to anyone who has read the paper that responses instead coming from assumed understandings or preconceived notions about the RSPT or the paper will not hold up or even be relevant after reading the paper.

Completely presumptuous  nonsense!

Answer the questions I raised or go elsewhere to spout your propaganda. 

<Right Step Periodic Table (RSPT) - response overview v6.pdf>

[Rene]

On 20 Aug 2025, at 07:53, Scott Hutcheon <scotth...@gmail.com> wrote:

Please respond to or raise issues with the attached v6 paper. For anyone who has read earlier versions, only the last few pages of Section 1 and Section 3 have been updated and expanded.

Scott, the paper has now expanded to an unwelcome 43 pages.

As I understand it, the RSPT appears to be driven by one central aim: to show the periodic table as a strict right-step unfolding of the Aufbau sequence, with no block displacements or footnotes. That's consistent in its own logic, but the trade-off is that chemistry disappears into flawed physics.

Gains: logical sequence, no footnotes, strict adherence to orbital order.

Losses: chemical coherence, pedagogical clarity, usability.

In short, the RSPT might make sense as a theoretical model of orbital filling, especially if you accept the “sloppy” version of the Aufbau principle popular in textbooks, but as a practical periodic table of chemistry my concerns stand: it undermines the very regularities that make the table useful.

It looks pretty, as I’d expect a right-step table to do, but as a depiction of the periodic law the gain in appearance is not worth the loss in chemical utility and didactic value.

The chemist’s version of the RSTP doesn't address the unfounded mixing of d- and f-block chemistry across 10 groups, nor the separation of 4d and 5d metals, nor the inexplicable splitting of the noble metals into two patches.

I commend your ambition of realising a right-step table but not its execution.

René

[ERIC SCERRI]

Hi Rene

Thank you for citing the term 

“Sloppy aufbau” which I coined 13 years ago in an article in the UK journal Education in Chemistry

Regards

Eric Scerri

On Aug 20, 2025, at 1:17 AM, Rene <re...@iinet.net.au> wrote:



[Mario Rodriguez]

I wouldn’t be too harsh on the Aufbau principle. It can be ammended with 2 rules:

1. Stability of half- and fully-filled d and f orbitals: d4 and d9 tend to capture 1e from the s orbital to achieve d5 (half-filled) and d10 (fully-filled). f8 expels 1e to the d orbital, resulting in f7 (half-filled). The only exception is wolfram, which follows the regular filling.

2. f orbitals never begin filling. The first electron goes into a d orbital. This d1 persists for the first two lanthanides and the first five actinides, before this electron is reclaimed by the f orbital. The only exception is thorium, which is d2.

Beyond these two rules (and their two exceptions), only palladium (which fills d10 before silver) and platinum remain as additional exceptions.

Mario RP

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[ERIC SCERRI]

Hi Rene. 

The sloppiness that I coined refers to something altogether different from all that you write below.   Have you ever read it?

Eric

On Aug 20, 2025, at 8:01 AM, Mario Rodriguez <mavo...@yahoo.es> wrote:



I wouldn’t be too harsh on the Aufbau principle. It can be ammended with 2 rules:

1. Stability of half- and fully-filled d and f orbitals: d4 and d9 tend to capture 1e from the s orbital to achieve d5 (half-filled) and d10 (fully-filled). f8 expels 1e to the d orbital, resulting in f7 (half-filled). The only exception is wolfram, which follows the regular filling.

2. f orbitals never begin filling. The first electron goes into a d orbital. This d1 persists for the first two lanthanides and the first five actinides, before this electron is reclaimed by the f orbital. The only exception is thorium, which is d2.

Beyond these two rules (and their two exceptions), only palladium (which fills d10 before silver) and platinum remain as additional exceptions.

Mario RP

En miércoles, 20 de agosto de 2025, 12:55:21 CEST, ERIC SCERRI <sce...@g.ucla.edu> escribió:

Hi Rene

Thank you for citing the term 

“Sloppy aufbau” which I coined 13 years ago in an article in the UK journal Education in Chemistry

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<109409_p024_eic-aufbau_thumb.jpg>

[ERIC SCERRI]

Sorry René. I meant to respond to what Mario wrote. 

On Aug 20, 2025, at 9:42 AM, ERIC SCERRI <sce...@g.ucla.edu> wrote:



[ERIC SCERRI]

Mario,

You also did not mention that as many as 6 of the 10 elements in the 2nd row of the d-block show anomalous electronic configurations.

I don't think your attempt to exonerate the Aufbau covered that.

Here is an article that considers an explanation for the anomalies in the d-block.

[Scott Hutcheon]

Again, not reading the paper guarantees incorrect assumptions (just as artificial periodic tables lead to artificial connections). The RSPT is not based on the Aufbau Principle (a principle with exceptions) but on the universal reality of atomic numbering and natural orbital filling (which, for less-specialized understandings often includes the more-generalized Aufbau Principle). It also elegantly shows where the Madelung Rule breaks down.

As for reading, it has been mentioned several times in this discussion that only Section 1 and Section 3 are relevant for this group with its deeper knowledge of periodic tables (the far larger Section 2 can be ignored) -- and that Section 1 and 3 have many graphics which intentionally makes for a quick read.

Per propaganda, the RSPT paper continually cautions against supporting the propagandistic efforts of insisting on or defending local beliefs or (pet) theories over universal scientific truths. While we can never achieve full objectivity (it's the fruitful journey towards an impossible destination) it is this ongoing goal that has allowed science to triumph over religions and pseudo-philosophies when the objective is greater than subjective (the universal over the local) -- though the paper also raises concerns about how this drive is recently devolving/regressing including accepting and even venerating a standard periodic table that is 92–100% incorrect for universal reality (as is the Left-Step) in exchange for mere local convenience and expediency.

Propaganda is undermined in the paper even regarding the puzzling insistence of maintaining the misnomered somehow romantic term "Noble" gases -- a term based on unscientific legacy eugenic beliefs about nobility despite the reality that nobles are inbred inferior genetic garbage... whose only apparent aspirational qualities are inexplicably unearned wealth, status, and effortless privilege (?).

The RSPT is rebuilt from the ground up (reverse engineering elemental evolution which uncoincidentally turned out to exactly match relative energy orbital filling) by assuming only two things:

1. the ordering of elements based on sequential atomic numbering (Z) of nuclei relative energy period shells and proton-neutron orbital filling from which the least complex (Hydrogen) to the much more complex elements (and their isotopes) arise -- recognizing that such ordering may change if Z passes a certain threshold (per Pyykkö's purely theoretical work); and

2. that characteristic chemical periodic similarities emerge/arise from the physical periodicities of relative energy period shells and electron orbital filling.

For those worried about this discussion also devolving, there are no concerns as it was always expected that the first fully scientific table would trigger emotional responses: “All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident.” -- author unknown, paraphrased from Schopenhauer

As well, if the RSPT paper is guilty of anything, it's probably of being too stereotypically Canadian by adhering to the following advice: “Always remember that to argue is to try and break down the reality of the person you are arguing against. It is painful to lose or change even the smallest part of one's reality, so be kind, especially if you might be right.” – paraphrased from Haruki Murakami

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Eric Scerri

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On Aug 20, 2025, at 7:59 AM, Mario Rodriguez <mavo...@yahoo.es> wrote:

I wouldn’t be too harsh on the Aufbau principle. It can be ammended with 2 rules:

1. Stability of half- and fully-filled d and f orbitals: d4 and d9 tend to capture 1e from the s orbital to achieve d5 (half-filled) and d10 (fully-filled). f8 expels 1e to the d orbital, resulting in f7 (half-filled). The only exception is wolfram, which follows the regular filling.

2. f orbitals never begin filling. The first electron goes into a d orbital. This d1 persists for the first two lanthanides and the first five actinides, before this electron is reclaimed by the f orbital. The only exception is thorium, which is d2.

Beyond these two rules (and their two exceptions), only palladium (which fills d10 before silver) and platinum remain as additional exceptions.

Mario RP

En miércoles, 20 de agosto de 2025, 12:55:21 CEST, ERIC SCERRI <sce...@g.ucla.edu> escribió:

Hi Rene

Thank you for citing the term 

“Sloppy aufbau” which I coined 13 years ago in an article in the UK journal Education in Chemistry

Libre de virus.www.avast.com

<109409_p024_eic-aufbau_thumb.jpg>

[ERIC SCERRI]

On Aug 20, 2025, at 9:57 AM, Scott Hutcheon <scotth...@gmail.com> wrote:

this discussion also devolving, there are no concerns as it was always expected that the first fully scientific table would trigger emotional responses: “All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident.” -- author unknown, paraphrased from Schopenhauer

Actually the first step is to get the idea published so that its acceptance extends to more people than just it’s creator!

As well, if the RSPT paper is guilty of anything, it's probably of being too stereotypically Canadian by adhering to the following advice: “Always remember that to argue is to try and break down the reality of the person you are arguing against. It is painful to lose or change even the smallest part of one's reality, so be kind, especially if you might be right.” – paraphrased from Haruki Murakami

Apologies for seeming to “break down” your reality, Canadian or otherwise.  Another quality you omitted to mention was the ability to respond to criticism.  This is what may just happen if you ever progress to even submitting it to a peer-reviewed journal.  

Eric

[Scott Hutcheon]

100% agree. The goal is always to eventually submit to a peer-reviewed journal where it can be falsified and verified (part of the reason for the success of science) -- and any assumption otherwise doesn't make sense. 

While I didn't originally submit the paper to this group, I'm grateful it was (and thankful for being accepted into the group) as the group discussion helps serve the function of a peer-reviewed preprint (though obviously better if the paper was read). 

René's feedback loops (without even reading the paper, but based on the original much less-developed basic LinkedIn article) have already started the bullet-proofing function required to expand and develop the paper, more thoroughly covering areas personally (and therefore incorrectly) considered obvious or self-evident after sitting with the RSPT for three years!

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[ERIC SCERRI]

On Aug 20, 2025, at 10:20 AM, Scott Hutcheon <scotth...@gmail.com> wrote:

100% agree. The goal is always to eventually submit to a peer-reviewed journal where it can be falsified and verified (part of the reason for the success of science) -- and any assumption otherwise doesn't make sense. 

While I didn't originally submit the paper to this group, I'm grateful it was (and thankful for being accepted into the group) as the group discussion helps serve the function of a peer-reviewed preprint (though obviously better if the paper was read). 

To be frank, I originally suggested that you join this group as a means of avoiding having to answer your questions and having to wade through your verbiage.  I am now regretting having done so.  

Of course you still have time to respond to my comments, in addition concentrating all your unrecognized and self-proclaimed genius on Rene’s valuable contributions.  

And thank you so much for informing us that the success of science is due to it’s falsifiability.  

Do you really think this is news to anybody here?

Eric

<Right Step Periodic Table (RSPT) - response overview v6.pdf>

[Mario Rodriguez]

Dear Eric,

Thank you for your prompt response. I am aware that the Aufbau principle has several exceptions, which is why I proposed refining it with two additional rules to minimize them. The question then becomes: what is the alternative? Should we abandon the Aufbau principle altogether and simply ask people to memorize the 118 electronic configurations? Or perhaps attempt to develop an entirely new predictive model for electronic configurations? and if so, what would those rules be?

We should keep in mind that many periodic properties also involve exceptions, and yet the periodic table (and all its variants) are accepted.

Regarding the f-block, I believe we agree that the combined rule, where f8 adjusts to f7 d1, along with the initial d1 for the first two lanthanides and five actinides, provides accurate predictions across this block, with the single exception of thorium (d2). Having only one exception in an entire block is, in fact, encouraging; and if someone can reconcile thorium, even better.

It seems, then, that the real challenge lies in the d-block. To clarify, I will list the elements along with their actual configurations, the standard Aufbau prediction, and "my" proposed correction (where the rules are that d4 s2 → d5 s1 and d9 s2 → d10 s1).

4                   Sc         Ti         V         Cr      Mn      Fe       Co     Ni          Cu        Zn

Real:          d1 s2   d2 s2   d3 s2   d5 s1  d5 s2  d6 s2  d7 s2  d8 s2  d10 s1  d10 s2

Aufbau:      d1 s2   d2 s2   d3 s2   d4 s2  d5 s2  d6 s2  d7 s2  d8 s2   d9 s2   d10 s2  2 Mismatches: Cr, Cu

Corrected:  d1 s2   d2 s2   d3 s2   d5 s1  d5 s2  d6 s2  d7 s2  d8 s2  d10 s1  d10 s2  No mismatches

5                    Y         Zr         Nb      Mo      Tc       Ru       Rh     Pd         Ag       Cd

Real:          d1 s2   d2 s2   d4 s1   d5 s1  d5 s2  d7 s1  d8 s1  d10 s0  d10 s1  d10 s2

Aufbau:      d1 s2   d2 s2   d3 s2   d4 s2  d5 s2  d6 s2  d7 s2  d8 s2   d9 s2   d10 s2  6 Mismatches: Nb, Mo, Ru, Rh, Pd, Ag

Corrected:  d1 s2   d2 s2   d3 s2   d5 s1  d5 s2  d6 s2  d7 s2  d8 s2  d10 s1  d10 s2  4 Mismatches: Nb, Ru, Rh, Pd

6                    Lu        Hf        Ta       W        Re      Os      Ir         Pt         Au        Hg

Real:          d1 s2   d2 s2   d3 s2   d4 s2  d5 s2  d6 s2  d7 s2  d9 s1  d10 s1  d10 s2

Aufbau:      d1 s2   d2 s2   d3 s2   d4 s2  d5 s2  d6 s2  d7 s2  d8 s2   d9 s2   d10 s2  2 Mismatches: Pt, Au

Corrected:  d1 s2   d2 s2   d3 s2   d5 s1  d5 s2  d6 s2  d7 s2  d8 s2  d10 s1  d10 s2  2 Mismatches: W, Pt

In the d-block, the Aufbau principle produces 10 mismatches, while my proposed correction reduces this to 6. In other words, Aufbau succeeds in 20 out of 30 cases (66.6%), whereas my correction achieves 24 out of 30 (80%).

Expanding the scope to the periodic table up to nobelium (102), the Aufbau principle correctly predicts 83 of 102 configurations (81.4%), while my correction accounts for 95 of 102 (93.1%).

Of course, there is still room for improvement. Additional refinements, or even an entirely new predictive model, are welcomed to further enhance the prediction of electronic configuration. I hope the alternative is not memorizing them.

Best regards,

Mario Rodríguez Peña (don´t blame René :) )

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On Aug 20, 2025, at 7:59 AM, Mario Rodriguez <mavo...@yahoo.es> wrote:

I wouldn’t be too harsh on the Aufbau principle. It can be ammended with 2 rules:

1. Stability of half- and fully-filled d and f orbitals: d4 and d9 tend to capture 1e from the s orbital to achieve d5 (half-filled) and d10 (fully-filled). f8 expels 1e to the d orbital, resulting in f7 (half-filled). The only exception is wolfram, which follows the regular filling.

2. f orbitals never begin filling. The first electron goes into a d orbital. This d1 persists for the first two lanthanides and the first five actinides, before this electron is reclaimed by the f orbital. The only exception is thorium, which is d2.

Beyond these two rules (and their two exceptions), only palladium (which fills d10 before silver) and platinum remain as additional exceptions.

Mario RP

En miércoles, 20 de agosto de 2025, 12:55:21 CEST, ERIC SCERRI <sce...@g.ucla.edu> escribió:

Hi Rene

Thank you for citing the term 

“Sloppy aufbau” which I coined 13 years ago in an article in the UK journal Education in Chemistry

Libre de virus.www.avast.com

<109409_p024_eic-aufbau_thumb.jpg>

ERIC SCERRI

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

 

 

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[ERIC SCERRI]

On Aug 20, 2025, at 12:07 PM, Mario Rodriguez <mavo...@yahoo.es> wrote:

Dear Eric,

Thank you for your prompt response. I am aware that the Aufbau principle has several exceptions, which is why I proposed refining it with two additional rules to minimize them. The question then becomes: what is the alternative? Should we abandon the Aufbau principle altogether and simply ask people to memorize the 118 electronic configurations? Or perhaps attempt to develop an entirely new predictive model for electronic configurations? and if so, what would those rules be?

Hola Mario!

Neither of these options is required, as I see it.  The aufbau is still a good approximation and in many cases does provide the correct overall configuration even if the order of filling is not strictly predicted with the exception of the s-block metals.

What I mean is that Sc, for example, in terms of filling order is [Ar] 3d1 4s2 whereas the aufbau gives [Ar] 4s2 3d1.  The overall result is the same.

The overall architecture of the PT is still provided by the n + l rule, but as has been noted there are about 20 exceptions.

We should keep in mind that many periodic properties also involve exceptions, and yet the periodic table (and all its variants) are accepted.

Yes

Regarding the f-block, I believe we agree that the combined rule, where f8 adjusts to f7 d1, along with the initial d1 for the first two lanthanides and five actinides, provides accurate predictions across this block, with the single exception of thorium (d2). Having only one exception in an entire block is, in fact, encouraging; and if someone can reconcile thorium, even better.

It seems, then, that the real challenge lies in the d-block. To clarify, I will list the elements along with their actual configurations, the standard Aufbau prediction, and "my" proposed correction (where the rules are that d4 s2 → d5 s1 and d9 s2 → d10 s1).

4                   Sc         Ti         V         Cr      Mn      Fe       Co     Ni          Cu        Zn

Real:          d1 s2   d2 s2   d3 s2   d5 s1  d5 s2  d6 s2  d7 s2  d8 s2  d10 s1  d10 s2

Aufbau:      d1 s2   d2 s2   d3 s2   d4 s2  d5 s2  d6 s2  d7 s2  d8 s2   d9 s2   d10 s2  2 Mismatches: Cr, Cu

Corrected:  d1 s2   d2 s2   d3 s2   d5 s1  d5 s2  d6 s2  d7 s2  d8 s2  d10 s1  d10 s2  No mismatches

5                    Y         Zr         Nb      Mo      Tc       Ru       Rh     Pd         Ag       Cd

Real:          d1 s2   d2 s2   d4 s1   d5 s1  d5 s2  d7 s1  d8 s1  d10 s0  d10 s1  d10 s2

Aufbau:      d1 s2   d2 s2   d3 s2   d4 s2  d5 s2  d6 s2  d7 s2  d8 s2   d9 s2   d10 s2  6 Mismatches: Nb, Mo, Ru, Rh, Pd, Ag

Corrected:  d1 s2   d2 s2   d3 s2   d5 s1  d5 s2  d6 s2  d7 s2  d8 s2  d10 s1  d10 s2  4 Mismatches: Nb, Ru, Rh, Pd

6                    Lu        Hf        Ta       W        Re      Os      Ir         Pt         Au        Hg

Real:          d1 s2   d2 s2   d3 s2   d4 s2  d5 s2  d6 s2  d7 s2  d9 s1  d10 s1  d10 s2

Aufbau:      d1 s2   d2 s2   d3 s2   d4 s2  d5 s2  d6 s2  d7 s2  d8 s2   d9 s2   d10 s2  2 Mismatches: Pt, Au

Corrected:  d1 s2   d2 s2   d3 s2   d5 s1  d5 s2  d6 s2  d7 s2  d8 s2  d10 s1  d10 s2  2 Mismatches: W, Pt

In the d-block, the Aufbau principle produces 10 mismatches, while my proposed correction reduces this to 6. In other words, Aufbau succeeds in 20 out of 30 cases (66.6%), whereas my correction achieves 24 out of 30 (80%).

Expanding the scope to the periodic table up to nobelium (102), the Aufbau principle correctly predicts 83 of 102 configurations (81.4%), while my correction accounts for 95 of 102 (93.1%).

Yes a paper carefully laying out this information could be useful especially in the educational context.

As was also mentioned in passing Pd is rather unique in being doubly anomalous as I like to call  it.

I chose Pd for my and my wife’s wedding rings because of this uniqueness.  Luckily she agreed to humor me.

I look forward to any thoughts you might have on my paper that essentially reports Eugen Schwarz’s way of ‘explaining’ the anomalies in a fundamental way that does not appeal to the half filled sub-shells are stable ‘nonsense'.

I can accept that a full shell might be stable, as in the case of the noble gases but where is it written that half-filled shells confer stability?  It’s not a principle of physics but just an ad hoc explanation which is given to beginning students.

To be more precise, a half-filled subshell is neither necessary nor sufficient for provided the lowest energy configuration.

There is nothing intrinsically stable about a half-filled sub-shell.  It so happens that for Cr, for example, 3d5 4s1 turns out to be more stable than 3d4 4s2 when all the various interactions are taken into account.

Sorry to keep saying this, but I have an article which deals with this topic among others,

[Scott Hutcheon]

Dare to dream! 

Per above unread discussions, Figures 7a, 7b, 7c, and 7d where electron affinity, electronegativity, ionization energy, atomic weight, and orbital-filling trends expect the corrected d- and f-period configurations. Chemistry evolves from Physics, a scientific pt has to support both.

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Eric

P.S.  

Completely separate point.  To base a periodic table on the fact that 3 particular radioactive elements align together is the height of folly in my view.

The periodic table is primarily about chemical reactivity not radioactivity.  Plus we certainly dont want to destroy well-known chemical periodicities at the expense of a single property such as radioactivity.  Not that anybody here would ever dream of doing this of course.  I’m just saying.   

[Mario Rodriguez]

Hi Eric,

Just answering few things regarding Aufbau,

- Yes a paper carefully laying out this information could be useful especially in the educational context.

REPLY: I take note. At the moment my life is going through some changes and I have very limited time to write, apart from long emails. Still, I’m keeping track to develop this further once things have settled. 

- I can accept that a full shell might be stable, as in the case of the noble gases but where is it written that half-filled shells confer stability?  It’s not a principle of physics but just an ad hoc explanation which is given to beginning students.

REPLY: In the d-block, this explains the transitions from d4 s2 to d5 s1 in chromium and molybdenum, and in the f-block, from f8 to f7 d1 in gadolinium and curium. Half-filled shells have all their orbitals occupied, though with one electron instead of the two found in fully filled shells. The only exception is wolfram. This phenomenon affects two elements in the d-block and two in the f-block, and I think it’s significant enough not to be dismissed. 

All papers are welcomed, as I always learn from them. Just to clarify, I’m the author of the periodic (square) spiral, which is based on chemical periodicity. I just commented in this thread about Aufbau.

Mario Rodríguez Peña

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P.S.  

Completely separate point.  To base a periodic table on the fact that 3 particular radioactive elements align together is the height of folly in my view.

The periodic table is primarily about chemical reactivity not radioactivity.  Plus we certainly dont want to destroy well-known chemical periodicities at the expense of a single property such as radioactivity.  Not that anybody here would ever dream of doing this of course.  I’m just saying.   

To view this discussion visit https://groups.google.com/d/msgid/PT-L/04846677-D6D5-499E-B8F4-A8B6B0F9E621%40g.ucla.edu.

[ERIC SCERRI]

On Aug 20, 2025, at 1:37 PM, Scott Hutcheon <scotth...@gmail.com> wrote:

Dare to dream! 

Per above unread discussions, Figures 7a, 7b, 7c, and 7d where electron affinity, electronegativity, ionization energy, atomic weight, and orbital-filling trends expect the corrected d- and f-period configurations.

This sentence doesnt even make sense.  What does it mean for something like electron affinity etc to “expect” some particular configuration?

Chemistry evolves from Physics, a scientific pt has to support both.

In general terms yers although you are expressing it in another odd way.  

But your table does harm to chemistry just in order to align some exotic raioactive elements.

[ERIC SCERRI]

On Aug 20, 2025, at 2:13 PM, Mario Rodriguez <mavo...@yahoo.es> wrote:

Hi Eric,

Just answering few things regarding Aufbau,

- Yes a paper carefully laying out this information could be useful especially in the educational context.

REPLY: I take note. At the moment my life is going through some changes and I have very limited time to write, apart from long emails. Still, I’m keeping track to develop this further once things have settled. 

- I can accept that a full shell might be stable, as in the case of the noble gases but where is it written that half-filled shells confer stability?  It’s not a principle of physics but just an ad hoc explanation which is given to beginning students.

REPLY: In the d-block, this explains the transitions from d4 s2 to d5 s1 in chromium and molybdenum, and in the f-block, from f8 to f7 d1 in gadolinium and curium. Half-filled shells have all their orbitals occupied, though with one electron instead of the two found in fully filled shells. The only exception is wolfram. This phenomenon affects two elements in the d-block and two in the f-block, and I think it’s significant enough not to be dismissed. 

Yes all this is very well known.  Please read my paper.  I am making a separate point.  

The posession of 1/2 filled subshell is neither necessary nor sufficient for enhanced stability over another possible configuration.

Said otherwise, posession of a half-filled subshell does not cause an atom to have an anomalous configuration

Here is the relevant secion from the article. 

The anomalous configuration of the chromium atom

The fourth idea that should be killed off, is that chromium displays an anomalous configu-ration of [Ar] 3d54s1 because of the stability of its half-filled sub-shell. Many chemistry textbook authors make this claim. My response is that there is nothing intrinsically stable about half-filled shells or sub-shells and that this is an ad hoc notion that should be abandoned. After all, why should the possession of a half-filled sub-shell confer any additional stability? What principle of physics is supposed to justify such a claim?

As a matter of fact, there is no such justification and it is just another myth that seems to be embraced by many chemical educators. As in the case of my earlier remarks concerning the concept of a solution having a pH of seven and whether it is neutral, there is an impli-cation that having a half-filled sub-shell is somehow both necessary and sufficient for an atom to display an anomalous configuration.

This implication can easily be demolished by answering two questions. Does a half-filled sub-shell lead to an anomalous configuration, in the sense of having an outer shell of ns1? The answer is no, since atoms such as manganese and technetium possess half-filled d sub-shells, yet they do not have outer shells consisting of ns1 configurations. Conversely, if a metal atom has an anomalous configuration, is this always accompanied by a half-filled sub-shell configuration? Once again, the answer is no. There are several metal atoms, especially in the second transition metal series, that are anomalous in displaying a 5s1 outer shell, that lack a half-filled 4d sub-shell. These atoms are niobium, ruthenium and rhodium with the following configurations respectively: [Kr] 4d4 5s1, [Kr] 4d7 5s1 and [Kr] 4d8 5s1. There is a lack of any direct causal link in both directions. Possessing half-filled sub-shells is neither sufficient nor necessary for there to be an anomalous configuration in any particular case. All that does exist is the coincidence that two atoms, namely chromium and molybdenum, among eleven atoms with anomalous configurations in the d-block, happen to display both attributes.

Why then do chemical educators continue to make such a ‘song and dance’ out of half-filled sub-shell stability in this context? Students still need an explanation for the anomalous configuration in atoms such as chromium. I suggest that given the choice between the following configurations [Ar] 3d5 4s1 and [Ar] 3d4 4s2 one can say that the first of these is observed because it is more stable overall. Better still, the second of these options is less stable because of the additional electron–electron repulsion between the two electrons in the 4s orbital. So, rather than falsely implying that there is something intrinsically stable about the half-filled sub-shell configuration, it is more accurate to say that this configuration occurs by default, since the other option represents a less stable arrangement of electrons.

The careful reader will note an apparent contradiction with what was stated in the earlier discussion about atoms such as scandium that favor having two electrons in the 4s orbital in order to achieve maximum stability. 

But each atom must be considered on its own terms. If anything, this emphasizes the fact that simple general rules concerning electronic configurations frequently break down. A fuller explanation of why  s1 configurations ever occur in preference to the more typical  s2 configurations can be found, again, in the work of Eugen Schwarz who has done so much to clarify the 4s, 3d question.10

[Mario Rodriguez]

Thank you for sharing this section of your paper. I had read it previously, and here are my thoughts on some specific points::

-  Does a half-filled sub-shell lead to an anomalous configuration, in the sense of having an outer shell of ns1? 

REPLY: These nomalous configurations don´t occur exclusively in the d block:

d4 s2 → d5 s1: Cr, Mo (but not W)

f8 → f7 d1: Gd, Cm

For some reason, in the middle of these blocks, anomalies appear trying to reach the half-filled d or f subshells. d subshells prefer to take 1 electron from the s orbital, while the f subshells prefer to push one into the d orbital, I guess for having proximal energies.

- The answer is no, since atoms such as manganese and technetium possess half-filled d sub-shells, yet they do not have outer shells consisting of ns1 configurations. 

REPLY: Mn and Tc already have configurations of d5 s2, so they do not need to pick or expel electrons to reach d5. The same applies to Zn to Hg, which already possess d10 s2 without requiring rearrangement. The elements that adjust to d10 by moving an electron are d9 s2 → d10 s1: Cu to Au.

- Conversely, if a metal atom has an anomalous configuration, is this always accompanied by a half-filled sub-shell configuration?

REPLY: The argument "half-filled subshells can´t explain all anomalies, then it can´t be the reason" is not valid as several reasons can explain anomalies. I proposed a Rule 1 “half- and fully-filled stability rule”, which explains 7 anomalies (4 involving half-filled, 3 involving fully filled), and a Rule 2 "in the f block, filling always begins with d1, which persists in the first 2 lanthanides and 5 actinides before being reclaimed by the f subshell". This trend explains 6 anomalies, with Th (d2) being the only exception. With these two rules combined, the number of anomalies can be reduced to 7.

- it is more accurate to say that this configuration occurs by default, since the other option represents a less stable arrangement of electrons.

REPLY: That is always correct, though it is not a predictive rule. The key question remains why a given arrangement is more stable than the alternatives.

Finally, regarding Sc, I must admit I am still not fully clear. If I understand correctly, the 4s orbital should be filled after 3d. But if we start filling 3d with 3 electrons, the configuration would be 3d3, leaving 4s unoccupied (since 3d can still hold 7 more). By contrast, if we begin with 4s, the configuration becomes 4s2 3d1, which is indeed the actual one. I openly acknowledge that I have not yet fully grasped this proposed modification to the Aufbau principle.

Mario Rodríguez Peña

https://groups.google.com/d/msgid/PT-L/BE0E4C50-30EA-4FD6-AEE5-64850544164B%40g.ucla.edu

.

[Mark Leach]

Hi All,

[Apologies… I don’t know if this came thru the first time of sending… I have now changed the subject line.]

For those who want a deeeeep dive into “anomalous” electronic structures of the elements, can I thoroughly recommend a YouTube workshop by Eric from the Covid years:

https://www.youtube.com/watch?v=5cfKot3nBFA

This really opened my eyes to scandium ionisation, “anomalous” electronic structures, exchange energies and the aufbau principle.

I always put “anomalous” in quotes because the electronic configurations are only anomalous with respect to an idealised Madelung’s rule, not with respect to nature itself.

Or, as T.H. Huxley put it: "the great tragedy of Science is the slaying of a beautiful hypothesis by an ugly fact.”

Mark

Mark Leach

meta-synthesis

[ERIC SCERRI]

On Aug 21, 2025, at 12:56 AM, Mario Rodriguez <mavo...@yahoo.es> wrote:

Thank you for sharing this section of your paper. I had read it previously, and here are my thoughts on some specific points::

-  Does a half-filled sub-shell lead to an anomalous configuration, in the sense of having an outer shell of ns1? 

REPLY: These nomalous configurations don´t occur exclusively in the d block:

d4 s2 → d5 s1: Cr, Mo (but not W)

f8 → f7 d1: Gd, Cm

For some reason, in the middle of these blocks, anomalies appear trying to reach the half-filled d or f subshells. d subshells prefer to take 1 electron from the s orbital, while the f subshells prefer to push one into the d orbital, I guess for having proximal energies.

- The answer is no, since atoms such as manganese and technetium possess half-filled d sub-shells, yet they do not have outer shells consisting of ns1 configurations. 

REPLY: Mn and Tc already have configurations of d5 s2, so they do not need to pick or expel electrons to reach d5. The same applies to Zn to Hg, which already possess d10 s2 without requiring rearrangement. The elements that adjust to d10 by moving an electron are d9 s2 → d10 s1: Cu to Au.

- Conversely, if a metal atom has an anomalous configuration, is this always accompanied by a half-filled sub-shell configuration?

REPLY: The argument "half-filled subshells can´t explain all anomalies, then it can´t be the reason" is not valid as several reasons can explain anomalies. I proposed a Rule 1 “half- and fully-filled stability rule”, which explains 7 anomalies (4 involving half-filled, 3 involving fully filled), and a Rule 2 "in the f block, filling always begins with d1, which persists in the first 2 lanthanides and 5 actinides before being reclaimed by the f subshell". This trend explains 6 anomalies, with Th (d2) being the only exception. With these two rules combined, the number of anomalies can be reduced to 7.

Thanks for your comments Mario, all of which seem correct to me.

I should say that I am not really interested in developing rules for electronic configurations in the way that you are suggesting.  After all, neither we nor students would ever need to predict the exact configuration of an atom, including the anomalous cases.

My interest is in the area of explaining the correct configurations of transition elements,

 including the long-standing 4s-3d question.

I’m also interested in more correct explanations for some anomalous configurations which do not just invoke 

“half-filled sub-shell stability”

I have posted several articles on these issues.

This is all discussed in detail in the workshop video.

- it is more accurate to say that this configuration occurs by default, since the other option represents a less stable arrangement of electrons.

REPLY: That is always correct, though it is not a predictive rule. The key question remains why a given arrangement is more stable than the alternatives.

Finally, regarding Sc, I must admit I am still not fully clear. If I understand correctly, the 4s orbital should be filled after 3d. But if we start filling 3d with 3 electrons, the configuration would be 3d3, leaving 4s unoccupied (since 3d can still hold 7 more). By contrast, if we begin with 4s, the configuration becomes 4s2 3d1, which is indeed the actual one. I openly acknowledge that I have not yet fully grasped this proposed modification to the Aufbau principle.

Yes, this is the obvious question that the account I present raises.  If 3d is more stable why does Sc not go 3d3 ?

The answer to this is also discussed in the workshop video of mine that Mark Leach kindly posted a link to earlier today.

A quick answer is, in order to minimize 3d-3d inter electron repulsion and given the relative size of the 3d and 4s orbitals.

Please watch the workshop video.

regards

Eric

[Rene]

On 22 Aug 2025, at 01:33, Mark Leach <ma...@meta-synthesis.com> wrote:

I always put “anomalous” in quotes because the electronic configurations are only anomalous with respect to an idealised Madelung’s rule, not with respect to nature itself.

Or, as T.H. Huxley put it: "the great tragedy of Science is the slaying of a beautiful hypothesis by an ugly fact.”

Nice quote Mark.

As Huxley intimates, tidy constructs—like the Madelung rule or the left-step table—can overlook messy details. But those so-called “ugly irregularities” are precisely what make the conventional periodic table so engaging (at least for the chemists); the split d-block is one such example.

Solid-state data underline this point: starting the f-block with La-Ac yields about 24 Madelung “violations,” or about 10 if you start with Ce-Th.

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1114

Nature apparently likes to make things interesting—evidently so that the philosophers among us have plenty of fuel for argument and don’t get bored.

René

[Mario Rodriguez]

Dear Eric,

Thank you for your reply. 

Just few remarks: if we know the correct explanation, then we can formulate more precise predictive rules as well. I find predictive rules fascinating, that’s why the periodic table exists, and here in Spain students are taught to predict electronic configurations. A precise Aufbau scheme is as valuable as a precise periodic table/spiral, especially since the table’s blocks correlate directly with Aufbau. After all, science is not only about explanations but also about using them to extrapolate/predict.

The 4s-3d topic is particularly interesting, and your workshop video is already on my to-do list. Unfortunately, my current time constraints (which affect also paper writing and other commitments) will delay when I can watch it in full. In the meantime, I would greatly appreciate specific answers, relevant paper extracts, or even references to the exact minutes in the video where these points are addressed.

My main interest is in turning correct explanations into more precise predictive rules (if explanations are not predictive by itself).

Regarding “half-filled subshell stability,” the observation that most d4 s2 atoms shift to d5 s1, and that all f8 shift to f7 d1, is striking. The common characteristic with full subshells is in both cases, all d and f orbitals are filled with either one or two electrons. It´s often explained that this produces symmetric charge distribution and maximizes exchange energy, as all orbitals have the same 1 or 2 electrons. This works well as a predictive rule, but I believe there is a real explanation as well. In science, we start with empirical patterns and then seek the underlying rationale.

Another point that puzzles me is scandium. It comes after two 4s elements, K and Ca. If Sc should start with 3d, the previous 4s should dissapear, then 3d orbital has to accept just 1 electron but not all 3, and then the last 2 electrons have to go again to 4s. The Aufbau works well predicting that after the 4s elements, the 3d series begins (as in the periodic table), and hence is 4s2 3d1. But to explain why the 4s electrons are lost first, perhaps it helps to note that shell 4 is outer to shell 3, and thus more easily ionized? Nonetheless, Sc ultimately shows a valence of 3, with all s2 d1 electrons removed when forming ions.

This email turned out longer than I intended. Apologies if you have already addressed some of these points elsewhere. Given my current situation, I would be very grateful if you could point me directly to a relevant paper section or specific video minute in case it´s already answered and you don´t need to write a specific response.

Thank you for your time,

Mario Rodríguez Peña

To view this discussion visit https://groups.google.com/d/msgid/PT-L/885EF870-E0C5-49D5-A3CF-38E51D7256C4%40g.ucla.edu.

[Mark Leach]

Hi All,

For those who want a deeeeep dive into “anomalous” electronic structures of the elements, can I thoroughly recommend a YouTube workshop by Eric from the Covid years:

https://www.youtube.com/watch?v=5cfKot3nBFA

This really opened my eyes to scandium ionisation, “anomalous” electronic structures, exchange energies and the aufbau principle.

I always put “anomalous” in quotes because the electronic configurations are only anomalous with respect to an idealised Madelung’s rule, not with respect to nature itself.

Or, as T.H. Huxley put it: "the great tragedy of Science is the slaying of a beautiful hypothesis by an ugly fact.”

Mark

Mark Leach

meta-synthesis

To view this discussion visit https://groups.google.com/d/msgid/PT-L/1831684307.2800110.1755762964780%40mail.yahoo.com.

[Mario Rodriguez]

Hi René,

You know I´m more inclined to consider d-block is not splitted by the f one. Let´s test both theories from their electronic configutations and deviations:

                                      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, and starting wifh f has 3 mismatches. This can be lowered to 2 if we consider the mid-block anomaly of half-subshell wannabes (f8 to f7 d1).

                                      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, and starting wifh f has 7 mismatches. This can be lowered to 6 if we consider the mid-block anomaly of half-subshell wannabes (f8 to f7 d1).

The lowest mismatches are achieved considering La and Ac within the f block and then d block starting with Lu and Lr, 3 in lanthanides and 7 in actinides, which can be lowered to 2 and 6 if we consider the mid-block anomaly of half-subshells wannabes.

Mario RP

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[Rene]

Thank you Mario

Yes, similar to you, Stewart (2018, p. 117) observed that an argument for lutetium in Group 3 was that the pth element in the 4f-series, with the exception of Gd, has p (for place) f-electrons.

In contrast, Wulfsberg (2006, p. 3) opined that:

…valence electron configurations of atoms and ions are also important in predicting the periodicity of chemical properties. Since ions are more important than isolated gaseous atoms for nearly all atoms, and important ions have no anomalous electron configurations, there is little reason to worry students with anomalous electron configurations of atoms: we prefer to teach ‘characteristic’ electron configurations without anomalies in the occupancies of d- and s-orbitals in the transition elements or d-, s-, and f- orbitals in the inner transition elements.

Thus, with lanthanum in Group 3, the number of f-electrons in the trivalent cations of the 4f elements corresponds perfectly with their position in that block. The series starts with Ce^3+ as [Xe]4f1 and concludes with Yb^3+ [Xe]4f13 and Lu^3+ [Xe]4f14.

As well, the f-electron induced lanthanide contraction starts at Ce and culminates at Lu.

Furthermore, each block starts with the appearance of the first applicable electron: s- at H, p- at B, d- at Sc, and f- at La.

I suggest that things do not get much simpler than that.

René

• Stewart PJ 2018, Tetrahedral and spherical representations of the periodic system, Found. Chem., vol. 20, pp. 111–120.
• Wulfsberg GP 2006, Periodic table: Trends in the properties of the elements,  in Encyclopedia of Inorganic Chemistry, 2nd ed., John Wiley & Sons, New York

[Jess Tauber]

The ancient astronomer Ptolemy dealt with anomalous planetary orbital patterns of the then-known planets with his epicycles, which dominated Western thinking for centuries until Renaissance workers figured out how apparent planetary orbital reversals were generated due to the particular relative positional perspective of earthly observers. In 19th century historical linguistics, with rules of sound change adduced for Indo-European languages, a  number of glaring exceptions had confounded their understanding, until some showed that many of these exceptions operated under their own rules, subsidiary to the major one(s), like lfeedback loops in a 20th century computer program, organized hierarchically.  Such rule hierarchies seem to be quite common. I'm not sure I want to say they are themselves the 'rule'... ;)

Jess Tauber

tetrahed...@gmail.com

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[Rene]

Thanks Jess.

The Madelung rule strikes me as functioning in a similar way. It doesn’t—at least as I understand it—account for the anomalies introduced via things like electron-electron repulsions in multi-electron atoms, spin-orbit coupling, or relativistic effects.

Yet it works remarkably well, because after each anomaly the pattern promptly (or eventually) re-emerges.

As Eric notes, “The level at which a science operates is a question for its practitioners, and the deepest, most fundamental bases are not necessarily the best for all purposes” (Scerri 2021, p. 132). The Madelung rule is an example of something that works well without operating at the deepest fundamental level.

Appropriately enough, the left-step periodic table is intended to reflect a more fundamental orbital ordering (see https://link.springer.com/article/10.1007/s40828-021-00157-8), yet it garners relatively little practical use.

Scerri ER 2021, The Periodic Table: Its Story and Its Significance, 2d ed., Oxford University Press, New York

René

[Rene]

Hi Mario

We may propose a new Group 3 rule:

"The third member of Group 3 is La."

The rule is based on (1) consistency with the number of f-electrons in the trivalent cations of the 4f elements; (2) the Ln contraction starting at Ce and culminating at Lu i.e. from the start to the end of the f-block; and (3) each block starting with the appearance of the first applicable electron.

As an added bonus, La Z = 57 = 5+7 = 12 = 1+2 = 3. La in group 3 is thus written in the numbers.

Lu, by contrast, meets none of these criteria (Z = 71; 7 + 1 = 8).

I quite enjoyed writing this email 😀

René

[Rene]

Re the proposed Group 3 rule, few people appreciate https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1157 as a particularly compelling physics-informed argument in the ongoing debate about the composition of Group 3.

The contrast between La in Group 3 v Lu in Group 3, having regard to the 4d to 5d trend in the d-block is remarkable.

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[Mario Rodriguez]

Hi René,

Your point 3 “each block starting with the appearance of the first applicable electron” can be falsified with Lr itself. Its real configuration is [Rn]5f14 7s2 7p1, which according to your rule would make Lr the start of the p-block. However, we don’t classify Lr as p-block. I prefer instead to view the beginning of some blocks in heavy atoms as irregular. If you consider La and Ac as irregular starts of the f-block and Lr as irregular start of the d block, the number of anomalies is reduced compared with the alternative (as I argued earlier). So, point 3 falsified. If you have to make an exception of point 3 with Lr, you can also do it with La and Ac. Furthermore, the previous element of Hf [Xe] 4f14 5d2 6s2 in a logical sequence would be Lu [Xe] 4f14 5d1 6s2 rather than La [Xe] 5d1 6s2.

Now, regarding point 1, "consistency with the number of f-electrons in the trivalent cations of the 4f elements; The series starts with Ce^3+ as [Xe]4f1 and concludes with Yb^3+ [Xe]4f13 and Lu^3+ [Xe]4f14". 

It is true that lanthanides most often appear in the +3 state, but we cannot ignore that Ce, Nd, and Tb can also reach +4, along with other less common valencies. Furthermore, whether La is taken as [Xe]6s2 5d1 or the hypothetical [Xe]6s2 4f1, it becomes La +3 = [Xe] in any case.

When we move to actinides, we have a big problem as trivalent cations are not common:

Ac +3 is [Rn], ends up in a p orbital, so because this ion doesn´t have an f orbital then it is not in the f-block according to your rule. However, if it would come from a hypothetical [Rn]7s2 5f1 the electronic configuration of Ac +3 would be the same, as with La.

Th +4 is [Rn] so no f orbital in this ion, then is not f block

Pa +5 is [Rn[ so no f orbital in this ion, then is not f block

Regarding U, the main cation is +6 so again [Rn]... the ions of these guys don´t want to be in the f block

Np +5 is [Rn] f2, so then it should be the second in the f block, and this block should start with U?

Pu +4 is [Rn] f4, so then f block should start in Pa?

So point 1 is also falsified, not only for the aforementioned reasons, but also because other blocks contain elements with multiple oxidation states without a main one. Which would be the “main” one for V (+2, +3, +4, or +5)? For Cr (+2, +3, or +6)? For Fe (+2 or +3)?

Two points falsified, while my position of considering La and Ac as f-block to reduce anomalies at neutral configurations, still stands. You also noted that Stewart (2018, p. 117) supports the same reasoning.

Of course, there are more interesting excerpts in the literature. I won’t cite Jensen´s papers since we know his stance :)

Chapter 2 “the debate on group 3” (Neve, F.: Chemistry of superheavy transition metals. J. Coord. Chem. 7(17–18), 2287–2307 (2022)):

“The second problem related to the atomic ground-state configuration of Lr may soon find a solution within the frame of international bodies on chemical nomenclature. If the 18-column periodic table is there to stay, then the most likely suggestion from the IUPAC panel working at the constitution of group 3 could be that shown in Figure 1 as recently mentioned in a provisional report [11b]. This version of the table has a complete group 3 (which compares to the actual IUPAC-agreed half-filled group) with Lu and Lr as the heaviest members. The natural consequences of this choice would be rather profound including an update of the d-block. The change would impact on the definition of both lanthanide and actinide series (and, of course, on the composition of the f-block) which were born as concepts but still are also conventions. If agreed on, the current 15-element series (including the eponyms) will make space for 14-element ones (La–Yb and Ac–No, respectively), therefore clearing the way for Lu and Lr to initiate the 5d and 6d series (Lu is 5d1 6s2, Lr is 7s2 7p1 but it would be 6d1 7s2 without relativistic effects including large spin-orbit splittings [12]).”

Don´t miss figure 1

Chapter “Lutetium or lanthanum above yttrium” (Winter, M.J.: Chemdex: Quantification and distributions of valence numbers, oxidation numbers, coordination numbers, electron numbers, and covalent bond classes for the elements. Dalton Trans. 53, 493–511 (2024)):

“The trends for the corresponding average CN values of groups 4–7 elements are reminiscent of the Sc–Y–Lu trend and on that basis Lu is better placed beneath Y rather than La in a chemical periodic table based upon VN and CN.” 

Don´t miss figure 15 either

"Strub, E., et al.: Pertechnetates– A Structural Study Across the Periodic Table. Chem. Eur. J. 30, e202400131 

(2024)"

Finally, the bond lengths of perrhenates and pertechnetates of Sc, Y, La and Lu shall be compared (Figure 30).

These are again very similar for the pertechnetates and the perrhenates. It also reflects that bond lengths as well as crystal radii of the Lu and Y compounds are very similar, as would be expected for any 4d/5d element pair. In this sense, our data

might be a humble contribution to the ongoing discussion as to whether La or Lu (and Ac or Lr, respectively) should be  placed beneath Sc and Y in the periodic table. Considering our data, we widely agree with the view of:[69–71] The main obstacle

of placing Lu underneath Sc and Y is the reluctance to display the periodic table in its 32-column form. Consequently, as there

is also evidence that Lr is a Lu homologue,[72,73] it may be hypothesised that Lr(TcO4)3 will also fit this trend. A 32-column

periodic table representing the bond lengths of all known metal pertechnetates is shown in the SI."

"From the early transition metals, Sc and Y serve as lighter homologues for lanthanoid elements, in particular the heavier lanthanoids. They support the placement of Lu in the periodic table underneath Y"

Don´t miss the graphical abstract.

A YouTube video of Prof. Poliakoff: https://www.youtube.com/watch?v=J1zNbWJC5aw

And finally, I think that the ugliness of splitting the d-block (as Eric remarked) outweighs the appeal of the numerology of La based on its Z :)

I also enjoy these exchanges, even if my messages tend to be quite long!

Mario RP

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[Jess Tauber]

Just because a space isn't filled doesn't mean it isn't there. That's how I deal with spin-orbit splitting for s in nuclear shells. S1/2 contains 2 nucleons (always one more than the numerator of the spin value). Hypothetical s-1/2 would thus have zero nucleons, and be empty.  We can deal with orbital shifts with regard to anomalous configurations in a similar fashion. The orbital is still there even if nothing fills it, at least with regard to structural bookkeeping.  Similarly, nuclear intruder levels are shifted from where they *should* be relative to simple harmonic oscillator LS structure, but are STILL regarded as belonging to the donor orbital.

To view this discussion visit https://groups.google.com/d/msgid/PT-L/1496759070.1586725.1756157176993%40mail.yahoo.com.

[Larry T.]

Quantum mechanics is about probabilities. An electron can be anywhere, it is just slightly more probable to find it in one unfilled orbital than in another.

To view this discussion visit https://groups.google.com/d/msgid/PT-L/CAO6d3hJxbATjjuFOfvyS7pATwUtVr-DMBbWEnS_GbNoJ_ioCNQ%40mail.gmail.com.

[Rene]

Thanks Mario. I've trimmed some of your thoughts so I can focus on the key issues.

To recap, the subject matter is the proposed Group 3 rule i.e. "The third member of Group 3 is La", based on: 

1. consistency with the number of f-electrons in the trivalent cations of the 4f elements;

1. the Ln contraction starting at Ce and culminating at Lu i.e. from the start to the end of the f-block; and

1. each block starting with the appearance of the first applicable electron.

On 26 Aug 2025, at 07:26, 'Mario Rodriguez' via Periodic table mailing list <PT...@googlegroups.com> wrote:

Your point 3 “each block starting with the appearance of the first applicable electron” can be falsified with Lr itself.

Not so. Point 3 refers to the first appearance of the relevant electron as the place at which the block concerned starts, and is subtended. Thus s starts at H; p starts at B; d starts at Sc; f starts at Ce. That is all there is to it. Subsequent irregularities in row starts are not relevant to this rubric. That e.g. Lr has a p-electron is not relevant.

La has the further advantage of incumbency in the d-block, since the 5d1 electron appears for the first time in its structure whereas it appears for the third time in lutetium, having already made a brief appearance in gadolinium.

Now, regarding point 1, "consistency with the number of f-electrons in the trivalent cations of the 4f elements; The series starts with Ce^3+ as [Xe]4f1 and concludes with Yb^3+ [Xe]4f13 and Lu^3+ [Xe]4f14". 

It is true that lanthanides most often appear in the +3 state, but we cannot ignore that Ce, Nd, and Tb can also reach +4, along with other less common valencies.

The +4 oxidation state of Ce, Nd and Tb is not relevant to the question of consistency in the trivalent cations of the 4f elements.

When we move to actinides, we have a big problem as trivalent cations are not common:

+3 is the only oxidation state common to all actinides.

Chapter 2 “the debate on group 3” (Neve, F.: Chemistry of superheavy transition metals. J. Coord. Chem. 7(17–18), 2287–2307 (2022)):

Neve sheds no light on the question. The IUPAC task group delivered only a provisional report, which IUPAC did not act on.

Chapter “Lutetium or lanthanum above yttrium” (Winter, M.J.: Chemdex: Quantification and distributions of valence numbers, oxidation numbers, coordination numbers, electron numbers, and covalent bond classes for the elements. Dalton Trans. 53, 493–511 (2024)):

“The trends for the corresponding average CN values of groups 4–7 elements are reminiscent of the Sc–Y–Lu trend and on that basis Lu is better placed beneath Y rather than La in a chemical periodic table based upon VN and CN.”

Winter notes that, "...a different study based upon sets of Sc, Y, La, and Lu compounds concludes there is no chemical basis for placing Lu beneath Sc and Y."

Winter is further selective in his choice of data points in that consistency in the trend of average CN values is limited to groups 4 to 6, out of ten transition metal groups. The trend for group 7 is more similar to that of Sc-Y-La. As well, the trend going down Sc-Y-La is similar to that going down Ca-Sr-Ba. This is relevant since the chemical behaviour of Group 3 generally resembles that of Groups 1–2 rather than that of Groups 4–11.

In contrast, as per my other email, the values of molar magnetic susceptibility (a physics-based property) reduce going down all groups of the d-block, and Sc-Y-La is more consistent with this trend.

"Strub, E., et al.: Pertechnetates– A Structural Study Across the Periodic Table. Chem. Eur. J. 30, e202400131 

(2024)"

Finally, the bond lengths of perrhenates and pertechnetates of Sc, Y, La and Lu shall be compared (Figure 30).

It also reflects that bond lengths as well as crystal radii of the Lu and Y compounds are very similar, as would be expected for any 4d/5d element pair. In this sense, our data might be a humble contribution to the ongoing discussion as to whether La or Lu (and Ac or Lr, respectively) should be  placed beneath Sc and Y in the periodic table. Considering our data, we widely agree with the view of:[69–71]

"From the early transition metals, Sc and Y serve as lighter homologues for lanthanoid elements, in particular the heavier lanthanoids. They support the placement of Lu in the periodic table underneath Y"

The trend going down Sc-Y-La appears more similar to that going down Ca-Sr-Ba. This is relevant since the chemical behaviour of Group 3 generally resembles that of Groups 1–2 rather than that of Groups 4–11.

A YouTube video of Prof. Poliakoff: https://www.youtube.com/watch?v=J1zNbWJC5aw

The Professor discusses the implication of the recent experimental measurement of the ionisation energy of lawrencium, and speculation this would support the placement of Lu and Lr in group 3 [thereby eliminating the possibility of a split d-block in long form depictions of the periodic table].

Regrettably, as per Jensen (2015), the ionisation energy of Lr has no particular bearing on its positioning in the periodic table.

As the Professor said, "What we're interested in is what Nature is like, not how easy it is to draw it." Hence, no elimination of a split d-block.

And finally, I think that the ugliness of splitting the d-block (as Eric remarked) outweighs the appeal of the numerology of La based on its Z :)

Ugliness is a subjective concept whereas in the case of numerology the numbers speak for themselves. I don’t see anything ugly in the attached image.

I also enjoy these exchanges, even if my messages tend to be quite long!

Mario RP

Yes, I look forward to your further thoughts in this matter.

Rene

[Larry T.]

"What we're interested in is what Nature is like, not how easy it is to draw it."

Yet, organizing is a part of human nature. Seeing nature as it is, without our natural ability to idealize would make our heads explode.

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[Mario Rodriguez]

Hi René,

There are not much to add as my points have not been falsified yet and several of your answers include adjectives such as "irrelevant" which is a personal opinion rather than an objective reason. Subjective affirmations can be replied with subjective responses. If you say it´s irrelevant for you, I can say it´s relevant for me. Anyway, I have no problem reminding my points in contrast to yours.

Regarding point 3, you say that the first element where an orbital appears is the most important and "Subsequent irregularities in row starts are not relevant to this rubric". Why do you think it´s more important the first element where an orbital appears than the overall match of the electronic configurations of all elements of that block? Do you consider the first element is special and cannot be anomalous ever? Why? In my opinion, I think that first element can be anomalous as any other one, so the overall match between theoretical an real electronic configuration of elements is more important. I already explained (and it has not been falsified yet) that:

1. The d1 electron appearing in La and Ac is reintegrated into f orbitals in Pr and Pu, leading to just 3 mismatches in electronic configuration of lanthanides and 7 in actinides, which can be lowered to 2 and 6 if we consider the mid-block anomaly of half-subshells wannabes. If you consider La out of the f-block and Ce as the first f block member, the mismatches rise to 11 for lanthanides and 10 for actinides out of 15. This level of mismatches should proof false any hypothesis and this is an objective reason.

2. The very same reintegration happens with the p1 electron in Lr that is claimed back to the expected d orbital in the following element Rf. This is also objective. When heavy atoms start a block seems to use the following subshell (d in case of f block and p in case of d block) and then this "rebel electron" is reclaimed by the "right" orbital at some point. g-block is also predicted not to start with a g orbital but d then f and then g (or even a first p) and then the "rebel electron/s" are being claimed black by the g orbital.

3. Finally, the previous element of f14 d2 s2 in a logical sequence is f14 d1 s2 not d1 s2. This is also objective.

I haven´t argued your point 2 in my previous email because I think that rules for the whole f block cannot be based only in lanthanides (the half of the f block). Rules must consider the whole block, including actinides. This criticism also affects your point 1 as it is only focused in trivalent cations of lanthanides.

"The +4 oxidation state of Ce, Nd and Tb is not relevant to the question of consistency in the trivalent cations of the 4f elements."

"+3 is the only oxidation state common to all actinides."

REPLY: You arbitrarily chooses the "relevant" and "irrelevant" oxidation states depending if it fits your rule 1.

Besides only considering lanthanides, on one hand you considers +3 as the "relevant" oxidation state because it´s the most commonly found and stable in lanthanides, disregarding other oxidation states, but in actinides other oxidation states are most commonly found and stable, so then you disregard these oxidation states as "irrelevant" by saying that +3 is the one shared by all actinides.

So, if we apply this "relevant/irrelevant" classification of oxidation states in the d block then it should be the most commonly found and stable, or the oxidation state shared by all elements in the whole period/row within the block? Or maybe the oxidation state that fits our rules?

Additionally, as I already said and it´s not yet falsified, La +3 [Xe] can come indistinctively from [Xe]6s2 5d1 or the hypothetical [Xe]6s2 4f1. Then, it doesn´t rule out their belonging to the f block. The same way that Ac +3, Pa +4, Th +5 and U +6 are [Rn], the cations of these actinides share the same electronic configuration and come from f block.

"This is relevant since the chemical behaviour of Group 3 generally resembles that of Groups 1–2 rather than that of Groups 4–11"

REPLY: So Group 3, within d block, has a chemical behaviour that resembles Group 1-2, within s block, rather than that of Groups 4-11, within d block? Actually, groups 11 and 12 are usually aligned to groups 1 and 2.

Prof. Poliakoff is basing his video in a Nature paper (a respectable source) from the same year 2015: https://www.nature.com/articles/nature14342. Also, by saying "What we're interested in is what Nature is like, not how easy it is to draw it" is not affirming "Hence, no elimination of a split d-block" as you said. Indeed, he´s far from agreeing with a split d-block. It depends on other reasons as said in that video and in this and my previous emails, coming from different sources and people besides me.

Finally, ugliness may be subjective but numerology is not science. Maybe regularity is a more objective reason supporting a continuous d-block (besides all the previous reasons), and very often regularity is perceived subjectively as beauty. We often say beautiful when we mean regular, a regular pattern, a regular face... Many thinkers studied the regular proportions behind aesthetic/beauty.

Mario RP

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[Rene]

On 28 Aug 2025, at 00:18, Larry T. <ora...@gmail.com> wrote:

"What we're interested in is what Nature is like, not how easy it is to draw it."

Yet, organizing is a part of human nature. Seeing nature as it is, without our natural ability to idealize would make our heads explode.

Thanks Larry. I laughed (in a good way) when I read your comment.

The context for the Professor’s statement is important. He was suggesting that maybe La goes under Y and Lr goes under La.

I interpret Poliakoff to mean that the classification should be grounded in what truly exists out there, not what fits nicely into our preconceived diagrams (the LSPT comes to mind) or what’s easiest to sketch or remember e.g. a conventional table with Lu-Lr in group 3.

In this specific context—deciding whether La-Lr belong under Y in Group 3—there’s no need to dramatize things: it's largely just a matter of chemical evidence, electron configurations, and historical precedent. The placement of He over Ne comes to mind. It diminishes the tidiness of the periodic table but the chips fall where they may. Thus: "“God made the initial conditions for the Big Bang such that the evolution of the universe would lead to many-electron atoms and a wacky s-block, in order that chemists and physicists would not be bored.”[i]

---

[i] Richard Feynman, in Bent H 2006, New Ideas in Chemistry from Fresh Energy for the Periodic Law. Author-House, Bloomington, Indiana, p. 140

If they do belong there (effectively no one believes this to the case) then that would be somewhat hard to draw.

René

[Jess Tauber]

'numerology is not science', eh? Maybe not when standing alone, but when based on actual measured experimental evidence, I believe it is. Witness Galileo's inclined plane experiments on acceleration, or Rydberg's analysis of atomic emission lines.  All of my own claims about Pascal Triangle combinatorics found in nuclear shell structures come from theories themselves based on actual experimental measurements. I don't just pull these numbers out of my ass. Dismissing and entire chain of reasoning with a nudge and a wink isn't going to win you many friends except amongst those who never think outside the box, the purveyors of orthodoxy.

To view this discussion visit https://groups.google.com/d/msgid/PT-L/129029931.2909112.1756328469827%40mail.yahoo.com.

[Mario Rodriguez]

Hi Jess,

Reading that the numerology thing is still resonating, I think I need to clarify some things.

Maths is a very respectable science, the basis of most of the other sciences, several millennia old, with several "daughter sciences", as geometry, symmetry...

However numerology, by definition, is the belief in an occult/mystical relationship between a number and coinciding events.

The reasoning I defined as numerology was the following: La belongs to Group 3 because if we add the ciphers of its Z (57) it would be 5 + 7 = 12 and in another round 1 + 2 = 3

There is no scientific meaning behind addition of ciphers of a number. They can even change if we shift from a decimal system to another one. But if this explanation is not enough, let's apply the same reasoning to Ac

Ac has Z (89) so if we add the ciphers it would be 8 + 9 = 17 and in another round 1 + 8 = 9. So Ac belongs to Group 9

Does the numbers speak for themselves then?

Maths works very well but if we apply other non-scientific meaning to numbers, aka numerology, then we run into false demonstrations. False premises leads to false conclusions.

Finally, I don't have any intention to create enemies, but be also sure that I will express my thoughts without any fear too. In the end, real friends accept the way you are/think.

Mario RP

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[Mario Rodriguez]

PS: I meant Ac has Z (89) so if we add the ciphers it would be 8 + 9 = 17 and in another round 1 + 7 = 8. So Ac belongs to Group 8. Still wrong

Mario RP

[Jess Tauber]

I submit that it all comes down to how we define a term and what our intentions are when using it.  All my own observations concern numerical patterns within data and the theories these help support

I've been criticized by people who cling to dogmatic views, often ignoring the detailed walk-throughs of my mathematical reasoning.  I make no claims about having any new basic observations of these phenomena, only the patterning of data produced by others. For some reason this appears to rub conventional thinkers, appealing to authority, the wrong way. There's a lot of sloppy thinking in the world, even among those who should know better.  I mentioned a few posts back that I'd found a new pure mathematical observation, having to do with the equations giving the powers of the metallic means (the infinitely large family of numbers to which the Golden Ratio/Mean belongs).  All I did was RECOGNIZE that the numerical coefficients that prefixed the terms in the equations were identical to the terms in a (2,1)-sided generalized Pascal Triangle that summed to Lucas numbers, while the powers these terms were raised to reflected the dimensionality of these Lucas-summing terms in the diagonals crossing through them parallel to the OTHER side of the Triangle. This dimensional effect has to do with the manner of packing, as of close-packed spheres, giving the values of terms within the diagonals.  This the outer edge of the classical Pascal Triangle, which is all ones, associates with zero-dimensionality, as it never changes. The diagonals containing the Natural numbers, is 1D, since the increase, as you descend the diagonal, is linear, monotonic.  The Triangular numbers reflect 2D, as you can generate them by close-packing spheres in a plane, as in a billiard ball rack. Tetrahedral Numbers go with 3D, close-packing spheres in a volume. And so on. My observations were summarily dismissed by the editor of the Fibonacci Quarterly on the grounds that they only publish those made by professionals. It didn't mean a thing that they were probably correct. That wasn't my first taste of orthodoxy resistance, but it was the most impactful personally.

[Larry T.]

Couple things I want to draw your attention to:

1) If La and Ac are place in Group 3, then f-block should begin with Ce and Th. Starting f-block with Ce and Th would make it different from three other blocks.

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=952

2) See attached paper by S. Alvarez.

Larry.

[ERIC SCERRI]

Dear Jess,

Many thanks for posting the article by Santiago Alvarez, whom I know.  But I was not aware of this article, which fully supports

my contention that Lu and Lr should be placed in group 3 rather than La and Ac.

Since Alvarez mentions the paper by my then student Will Parsons and me, I am enclosing a copy now.

[Jess Tauber]

Eric, I think you may have conflated me with Larry- I'll take that as a compliment. :)

Regrettably, IUPAC did not accept the recommendation that my working group and I made concerning group 3.  

This was published in the IUPAC magazine “Chemistry International”.  I believe I may have posted it a while ago, but here it is again,

Regards

Eric Scerri

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[Rene]

On 31 Aug 2025, at 14:47, ERIC SCERRI <sce...@g.ucla.edu> wrote:

Dear Jess,

Many thanks for posting the article by Santiago Alvarez, whom I know.  But I was not aware of this article, which fully supports

my contention that Lu and Lr should be placed in group 3 rather than La and Ac.

On Aug 30, 2025, at 6:38 PM, Larry T. <ora...@gmail.com> wrote:

Dear Eric, Larry

I can see two issues undermining Alvarez’s case for Lu in group 3.

The first is that his cross-row comparisons are placement-invariant: Lu looks 5d-like whether it sits under Y or ends the 4f row.

The second is that he privileges a down-group radius match with Group 4 (Sc–Y–Lu ≈ Ti–Zr–Hf; Sc–Y–La ≈ Ca–Sr–Ba), effectively adopting the rule “place similar columns together.”

In so doing, he overlooks three inconvenient truths: group 3 chemical behaviour aligns more with groups 1–2 than 4–11; groups 1–3 are predominantly ionic, whereas groups 4–5 are predominantly covalent; and characteristically transition-metal behaviour only first appears in group 4.

Thus, on the foundational recurrence of chemical behaviour, La under Y is the natural placement.

René

[ERIC SCERRI]

Thanks Rene,

I suggest you contact Alvarez and argue this out with him.  If you do so, please share any correspondence.

As I have stated before, neither chemical nor physical properties, such as electronic configurations, succeed in resolving this issue categorically.

The argument I published in the form of a recommendation from the working group does provide an almost categorical argument, and it depends on just two simple assumptions.

1.  Present the PT in 32-column format

2.  Insist on a smooth increase in Z across all periods.

The only fly in this ointment is the possibility of the split d-block periodic table, which as several people here have correctly stated

is a non-starter.

Eric Scerri