Döbereiner-Scerri Triads

[Scott Hutcheon]

Hello all, and apologies,

While I have been as guilty as anyone in denigrating triads in relation to the Periodic Table as mere numerology (a common reaction mentioned in one of Scerri's attached and related papers), with my recent ongoing recent research I finally decided to look into Scerri's work around triads.

As even a beginning student of the history of the periodic table should be fully aware, the monumental culmination of two streams of research leading to the 1913 breakthrough understanding of the periodic table involved: 

a) Dutch physicist Van den Broek's proposal and English physicist Moseley's confirmation that an element's atomic number was more fundamental than an element's atomic weight; and 

b) French physicist Becquerel, Polish-French physicist-chemist Curie, English chemist Soddy, and New Zealand physicist-chemist Rutherford's realization that radioactivity (and decay and isotopes) solved the other main structural component that drove the periodicity of the table -- later fully understood and confirmed by English physicist Chadwick's discovery of the neutron in 1932.

While it has confusingly been over 100 years for these 1913 understandings to be translated into the only two known periodic tables based on the atomic number (Z) and radioactivity (Column of Instability) of elements in relation to their periodicity -- though neither of them were discovered looking for radioactive periodicity, merely confirmed by its inclusion -- it is gratifying that the two scientific tables (uncoincidentally also the most two recent actual tables considering how science evolves) are also the tables that most fully support Scerri's recent work on rehabilitating the importance of the Döbereiner triad relationship within the Periodic Table.

Russian-American mathematician Beylkin's 2018 BPT-32 based on 4n2 periods (instead of the standard 2n2), contains the Column of Instability (mandatory since 1913, or at least since Seaborg's 1945 breakthrough, for any scientific table, and unknowingly included in this PT), and was introduced to us by our very own René (and his love of symmetry!) within Mark's incredible resource (https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=1202). 

The BPT-32 reduces the number of elements not included in triads to nine.

The RSPT-32, as is known from the original LinkedIn discovery article (https://www.linkedin.com/pulse/possibly-last-periodic-table-youll-ever-need-scott-hutcheon/), and the paper shared here, was reverse engineered by a Canadian amateur cosmologist-astronomer-physicist from elemental evolution within a new Emergent Universe model (where Information → Physics → Chemistry → Biology, without the need for any Catholic Priest Religious Belief "Proof of God" singularity). 

The RSPT-32 reduces the number of elements not included in triads to four.

Both the Beylkin and RSPT properly arrange the d- and f-periods, as opposed to the artificial d-block stacking of the d-periods by nearly every locally correct only PT, though the Beylkin splits the first two d-periods evenly to maintain symmetry (as opposed to a recent proposed splitting of just Sc-Y away from the d-periods to maintain Sc-Y-La-Ac in the Scylac-Scylur Skirmish).

Apologies again for not recognizing the relevance of triads earlier (and not placing it in the strategic overview paper), and please find below the attached PDF showing the progression down to four non-triad elements with the various known PTs, and then some of Scerri's invaluable research around triads (as well as Beylkin's paper). 

As for the last four outlier elements, see Scerri's work here and elsewhere regarding his proposal for the enhanced uniqueness effect of the first elements.

Thanks again for all your work on this, Eric. Though it will probably take many decades from now, your triads will eventually triumph and have the last laugh!

[Rene]

Scott

Thanks for the post—I have some observations regarding (i) the so-called column of instability, (ii) symmetry considerations, and (iii) the status of triads.

1. Column of instability

The recognition of a “column” or axis of instability does not seem to require rearranging the d- and f-periods. It emerges on standard periodic tables once the f-block is placed beneath its natural s-d-p alignment, e.g. with Pm and Np located under Mn in Group 7. Visualisations such as the following show this:

https://artsexperiments.withgoogle.com/periodic-table/

2. Symmetry
You mentioned "his [my] love of symmetry!" but I actually have no stake in symmetry or its absence per se. What concerns me is what Jensen warned against—the abuse of (Platonic) symmetry arguments when they override chemical facts (Jensen 1986 passim; 2003 pp. 953–954). Likewise, Scerri reminds us to be cautious with arguments based on regularity or symmetry (2020 pp. 387, 401). Symmetry can inform design, but should not dictate it.

3. Triads

There's been a lively debate here. Stewart (2018 p. 75) emphasises that triads arise from periodic structure and do not cause it. Jensen (2019) questioned the significance of vertical triads, prompting Eric to praise them (Scerri 2022).

Curiously, horizontal triads in the modern table reveal a striking chemistry-based regularity. With La in Group 3, there is a unique repeating pattern of maximum oxidation states (+2, +3, +4) across many consecutive element triplets up to at least fermium:

P  +2   +3   +4

2  Be   B    C

3  Mg   Al   Si

4  Ca   Sc   Ti

4  Zn   Ga   Ge

5  Sr   Y    Zr

5  Cd   In   Sn

6  Ba   La   Ce

6  Hg   Tl   Pb

7  Ra   Ac   Th

Whether this sequence continues to Cn-Nh-Fl remains an open question.

This regularity does not persist if Lu is placed in Group 3. Sc, Y, La, and Ac consistently occupy the middle position of these recurring horizontal triads, whereas Lu and Lr do not. For example:

• Yb (+3), Lu (+3), Hf (+4)—Lu does not occupy the middle position
• Nb (+3), Lr (+3), Rf (+4)—same issue

Dias (2004 p. 375) noted the importance of horizontal triads, and Scerri (2004 p. 138) wrote:

“Chemically similar groups should be close together, either as vertical groups or horizontal triads, with links between related elements clearly visible.”

Thus, in this specific and chemically grounded context—maximum oxidation states within horizontal triads—a table placing La (and Ac) in Group 3 yields greater regularity than placing Lu (and Lr) there.

Mendeleev may have been pleased given he used horizontal triads when predicting the properties of the then undiscovered elements Sc, Ga, and Ge.

René

• Dias, J.R.: The periodic table set as a unifying concept in going from benzenoid hydrocarbons to fullerene carbons. In: Rouvray, D.H., King. R.B. (eds): The periodic table: Into the 21st century, Institute of Physics Publishing, Philadelphia, 371–396 (2004)
• Jensen, W.B.: Classification, symmetry and the periodic table. Comput. Math Appl. 12, 487–510 (1986)
• —— The place of zinc, cadmium, and mercury in the periodic table. J. Chem. Ed. 80, 952–961 (2003)
• —— Trouble with triads. Program and abstracts, 258th ACS National Meeting San Diego, CA August 25–29. American Chemical Society. 13 (2019)
• Scerri, E.: The best representation for the periodic table: The role of the n + l rule and the concept of an element as a basic substance. In: Rouvray, D.H., King, R.B. (eds.) The periodic table: Into the 21st century, pp. 143–160. Institute of Physics Publishing, Philadelphia (2004)
• —— The Periodic Table: Its Story and Significance, 2nd edn. Oxford University Press, New York (2020)
• —— In praise of triads. Found Chem 24, 285–300 (2022)
• Stewart, P.J.: Tetrahedral and spherical representations of the periodic system. Found. Chem. 20, 111–120 (2018)

[johnmarks9]

Fascinating and thought provoking. Thanks Scott.

In the "other features" of Belykin´s PT, his fifth point that groups IVA, VA, VIA and VIIA "can still be traced". This is hardly the case which might be overcome by distinguishing Döbereiner triads (all same subshell) from Sommerfeld triads (cross subshells):

for:

Fe, Co, Ni etc. could be placed over Dy, Ho, Er to preserve the precious symmetry  .  .  .

Agree with your recognition of the importance of triads and Scerri´s resurrection of them.

[Julio Gutiérrez Samanez]

Dear Colleagues,

I just read Scott Hutcheon's post about triads and found it very interesting. It's very appropriate to apologize to Eric and agree with him; acknowledging mistakes is a gentlemanly act that enhances science. I think it's a lesson for everyone.

I found a typo in one place in Rene's response to Scott: it says Nb (41Nb) instead of No (102No). Well, the sequence should be 102, 103, 104; that is: (No, Lr, Rf).

On the other hand, placing Pm and Np under Mn means placing 25 Mn, and below this element, the pair: 61Pm and 93 Np. I believe this is inconsistent if we check it with my Z sequence (with Bend's colors), which I include below as an attachment.

In the standard Periodic Table, after 25Mn, follow 43TC, 75Re, 107…

The sequence 61Pm and 93Np could be included after 25Mn and 43Tc; but it is inconsistent because of the following argument: 43 – 25 = 18. If we take 18 as the pattern, then 43 + 18 = 61Pm, apparently correct; therefore, 61 + 18 = 79Au and 79 + 18 = 97Bk. This would be a serious error.

This is incorrect because the pattern changes for the fourth binode as follows: 93Np - 61Pm = 32; therefore, the pattern is no longer 18, but 32.

Then: 93 + 32 = 125, which would be an element of the hypothetical g-block.

In the figure attached as a file below, there is no way to find coherence between 61Pm and 93Np with the sequence 25Mn, 43Tc (separated by 18 elements) followed by 43Re + 32 elements = 75Re, in turn 75Re + 32 = 107…

Obviously, the pattern between 61 and 93 is 32 elements because they belong to the 4th binode, where 2N^2 = 32, when N (or any other conventional symbol) is the number of the binode, dyad, or pair of periods with an equal number of elements. After 93, we must add 2(5)^2 = 50 elements.

In any case, I agree with Scott that the value of the Döbereiner, Sommerfeld, and Scerri triads has not lost its validity. It doesn't contradict the "binodic" functions that complement Mendeleev's law, as corrected by Van den Broek and Moseley.

Thanks to Scott for referring to Beylkin, whose work I was unfamiliar with, and I see that we both reached the same conclusions (4n^2 instead of 2n^2), although I explained this in my 2004 book. In it, I paired or related: 4(sum n^2) with Z (concluding that the periodicity is by binodes, not by periods). Then, this year, 2025, I found the relationships of some increasing spiral functions that define chemical properties (colored by Henry Bend) as "periodic functions of the atomic numbers Z." With this tool or scope, many unknowns generated by triads should be clarified. It is true that "triads arise from the periodic structure and do not cause it" (Stewart 2018), but it is not true that the periodicity of the periodic table is "arbitrary," as Stewart claimed. Furthermore, increasing symmetry is observed in the periodicity, because the "pattern" grows with the binodes, and these change with the addition of a new azimuthal quantum number. I think that these three laws or mathematical functions of matter: (2n^2), (4n^2), Z = [4(Sum n^2)], define or "cause" the periodic structure. Perhaps I am wrong.

Warm regards from Cusco, Peru

Julio

(Please excuse my Google translation)

https://acrobat.adobe.com/id/urn:aaid:sc:VA6C2:fe58cf03-2442-4785-aa8a-c3c19f5b94ee

(99+) HARMONIC PERIODICITY OF THE CHEMICAL PROPERTIES OF THE CHEMICAL ELEMENTS (2025)

Periodical system (binodic form), new mathematical paradigm - YouTube

Binódic periodic system: a mathematical approach | Foundations of Chemistry

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[ERIC SCERRI]

The issue will appear very soon online and in print format.

[Scott Hutcheon]

Hello all, sorry, didn't realize I had only replied to Julio. Here is my original response from three days ago:

I was challenged to uncover a PT that contained Döbereiner-Scerri Triads for 100% of the elements.

Mark, please add the Right-step Triadic Periodic Table (RTPT-32) to your invaluable online reference database.

RTPT-32 Pros:

1) As expected of any scientific periodic table, the RTPT-32 incorporates most of the PT rules from the RSPT paper, including the mandatory Column of Instability (Mn–125, and related Island of Stability connection), as well as Schwarz's "backbone of the periodic table" with the connected Halogen Group (including H-Halogens as per René also), the He-Octet Gases Group, and the Alkali Metals and Alkaline Earth Metals Groups; and

2) It also contains the mandatory Sc-Y-La-Ac, as the Skylac-Skylur Skirmish is over (per the RSPT paper), as well as the B-Al-Sc-Y-La-Ac Group extension/relation that René has extensively researched, rehabilitated, and referenced; and

3) Resurrects the ghost of octaves, albeit in a different way, though it does contain periods of 8-8-16-16-32-32.

4) As per the RSPT paper, the RTPT-32 continues the idea of later orbitals/charge densities 'pushing out' or displacing earlier orbital types, where here 4p and 5p are also displaced by 3d and 4d, and 6p and 7p are also displaced by 4f and 5f which naturally displaces 5d and 6d.

5) As far as I'm aware, this is the only table that satisfies Eric's research on triads, Renér research on the trends of the potential extended Group B-Al-Sc-Y-La-Ac, and the RSPT paper (as this is a modified version of the RSPT-32 and RSPT-36). So there was peace and much rejoicing in the village.

RTPT-32 Cons:

1) This PT entirely breaks up the traditionally stacked p-block into three p-periods:

• This follows the mandatory breakup of the d-block into separate d-periods for any scientific (universal) periodic table in order to correctly incorporate the Column of Instability (and related Island of Stability, as well as the proper relationship for the REE elements), however, it appears too radical based on electronic/charge density periodicities; and
  
  
• Not aware of research other than B-Al-Sc-Y-La-Ac justifying these p2 through p4-element headed Groups as sharing chemical and/or physical properties...
  
  
• Though this may be acceptable as p1- through p4-element groups of the p-block have always been an illogical and fundamentally unexplainable mixed-bag of chemically and/or physically unrelated elements, and René has provided detailed trend justifications for at least the p1-element headed Group containing B-Al-Sc-Y-La-Ac; and
  
  
• Resurrects the ghost of octaves, albeit in a different way, though it does contain periods of 8-8-16-16-32-32.
  
  
• Comes preloaded with the obvious dismissal as the Split-p or Split-p Soup table -- though it has precedent with the 1934 VRPT-32 (Victor Romanoff Periodic Table) split-d periodic table that interests René : https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=290

PTPT-16 (Perfect Triadic Periodic Table) aka the Maple Leaf Periodic Table (MLPT-16).

Since the discovery of the RTPT-32 a couple of days ago, naturally the challenge was then to find a 'perfect' triadic table where every single element exists within perfect triads both vertically and horizontally. 

As per the RSPT paper and the Bell Curve rule (where focusing entirely on one aspect or entirely ignoring one aspect leads to artificial tables), the only interesting bit for me about this curiosity is that the first naturally occurring radioactive element (Bismuth) forms a group with the first unnaturally occurring element (Einsteinium) -- though the expected Mn–125 Column of Instability forms with anti-rule artificial gaps in it (as Selenium and Tellurium and Iridium are not radioactive/unstable).

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On Thu, Oct 30, 2025 at 1:30 PM Scott Hutcheon <scotth...@gmail.com> wrote:

Hello all, I was challenged to uncover a PT that contained Döbereiner-Scerri Triads for 100% of the elements.

Mark, please add the Right-step Triadic Periodic Table (RTPT-32) to your invaluable online reference database.

RTPT-32 Pros:

1) As expected of any scientific periodic table, the RTPT-32 incorporates most of the PT rules from the RSPT paper, including the mandatory Column of Instability (Mn–125, and related Island of Stability connection), as well as Schwarz's "backbone of the periodic table" with the connected Halogen Group (including H over Fl as per René also), the Octet Gases Group, and the Alkali Metals and Alkaline Earth Metals Groups; and

2) It also contains the mandatory Sc-Y-La-Ac, as the Skylac-Skylur Skirmish is over (per the RSPT paper), as well as the B-Al-Sc-Y-La-Ac Group extension/relation that René has extensively researched, rehabilitated, and referenced; and

3) Resurrects the ghost of octaves, albeit in a different way, depending on whether one is a fan or not.

RTPT-32 Cons:

1) This PT entirely breaks up the traditionally stacked p-block into three p-periods:

• This follows the mandatory breakup of the d-block into separate d-periods for any scientific (universal) periodic table in order to correctly incorporate the Column of Instability (and related Island of Stability, as well as the proper relationship for the REE elements), however, it appears too radical based on electronic/charge density periodicities; and
  
  
• Not aware of research other than B-Al-Sc-Y-La-Ac justifying these p2 through p4-element headed Groups as sharing chemical and/or physical properties...
  
  
• Though this may be acceptable as p1- through p4-element groups of the p-block have always been an illogical and fundamentally unexplainable mixed-bag of chemically and/or physically unrelated elements, and René has provided detailed trend justifications for at least the p1-element headed Group containing B-Al-Sc-Y-La-Ac; and
  
  
• Resurrects the ghost of octaves, albeit in a different way, depending on whether one is a fan or not.
  

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[johnmarks9]

Brilliant, Mr Hutcheon!

Do you think you need the initial steps down? After all, the first "period" is just an artefact of the Bohr-Sommerfeld model.

Also, to make the table convenient (18 columns instead of 32), the 5d transition series (Lu - Hg) could be slotted under the initial ten 4f:

My colours preserve the Mendeleyev groupings but do you think these could be better displayed by extending them to 4f and 5f? For example, what chemical evidence would there be for grouping terbium with gold? Or lavoisium (aka dysprosium) with mercury? Does spectrium (aka ytterbium) ever show a valency of 6 or -6?

Congratulations on the Hutcheon Triadic PT!

[Scott Hutcheon]

Hello John, and thanks for the response!

I truly appreciate your creative idea of finding an original workaround for the Scylac-Scylur Skirmish that satisfies both camps by Grouping B-Al-Sc-Y-La-Lu-Ac-Lr (at least that's what I'm guessing was the impetus behind it):

However, this leads to issues addressed in the RSPT paper:

1) This continues the ongoing desire to artificially stack the d-periods into a solid d-block (though at least yours is much more novel and interesting by interspersing the f-periods between broken up d-periods). Per the paper, I would suggest that it also does not contain the Column of Instability as Re (Rehnium) is not radioactive/unstable (and the instability/radioactivity trend should increase down the Group).

1a) The blasphemy/sacrilege of breaking apart the sacrosanct d-block into their more scientific (universal) d- and f-period relationships has been why there has been no scientific periodic tables up until the Beylkin in 2018 and the RSPT in 2021 -- despite the first step initial attempts with the 1934 VRPT-32 (Victor Romanoff Periodic Table) split-d periodic table: https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=290

1b) Devotees/adherents/zealots of the current standard religiously iconic PT (which is completely artificial/unscientific/incorrect for at least 92% of the universe), have been completely unable to imagine breaking up the d-block which is why we've been stuck with an unscientific formulation since at least 1945 with Seaborg. 

While 20/20 hindsight makes the Column of Instability seem blindingly obvious (per the attribution to Arthur Schopenhauer “All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident.”), there have been no known previous proposals or even references to such a self-evident Column of Instability and only halfhearted QM attempts to explain the seemingly random positions of Tc and Pm in the standard PT. 

While it's unbelievable that it took nearly 80 years for the Column (especially after the 1913 breakthroughs regarding atomic number and radioactivity) to be understood as a fundamental pillar for any scientific PT, it was simply a case of being unable to see (as I like to say) the fundamental forces for the decision trees, as obviously the iconic SPT-18 Mn-Tc-Re-Bh-artificial gap-Pm-Np manufactured 'column' is nowhere near the same as the Beylkin/RSPT/RTPT Mn-Tc-Pm-Np (and extended Mn–125). And obviously no such manufactured 'column' exists with the extended SPT-32 (the standard periodic table in its proper 32-column form), and would continue to be missed with an extended SPT-50 (the standard periodic table in its proper extended 50-column form) if g-period elements are added (as would the connection to the Island of Instability).

2) Per your realization, not sure if your proposed later new groupings would have chemical and/or physical property trends down the columns.

3) There are several other issues as discussed in the RSPT paper with this formulation, including artificial gaps in the first four Groups, but I would instead prefer (per the RSPT paper) to avoid displacing/collapsing periods as with the current standard PT (nominally for print width convenience but primarily for humanity's ocularcentric preference for visual bilateral symmetry) and instead truncating into a more compact step-down form (here the RTPT-18) for print convenience without breaking or obscuring periodic and group relationships (as two-element columns aren't considered enough to be classified as Groups with trends...

Which is also why, per the RSPT paper, the Sloppy Sandwich Suggestion of somehow proving d-periods should remain in an artificial stacked d-block by showing that less than half of the only two vertically grouped 4d- and 5d-elements (the sandwich filling) show related trends which reduces to near zero related property trends down the groups when including the same vertically grouped 3d- and 6d-elements (the sandwich bread slices) in the artificial d-block columns. 

Two elements (such as 4d and 5d) don't make a Group with trends.

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[johnmarks9]

Greetings, Scott.

The symmetry could be improved with:

but that still leaves the ugly gap before the 5d sandwich. However, the sp-block warrants splitting more than the d-block or the f-block.

It seems to me that Beylkin´s excellent 2018 PT achieves what you desire.

You make much of an axis of instability, centred around the Mn-Tc-Pm-Re-Np column though note that Re is not radioactive, but neither is Mn . . .  

Bohrium (Z = 107) is of course radioactive, and a regular extension of Mendeleyev would predict your "column of instability" would intersect 6f at Z = 143 and 7d at Z = 157. The new subshell (Z = 121-138) would be intersected at Z = 125. Do the atomic chaps peering into the far depths of aufspaltung see anything special in Z = 107, 125, 143 or 157?

Regards,

John

[Scott Hutcheon]

Thanks John, and yes the RSPT paper predicts that the single lone not-currently-considered-radioactive isotope of Mn (Manganese) will turn out to be around as unstable, at similar orders of magnitude, as the recently understood Bismith (Bi)!

However, coming to periodic tables from a cosmology interest, I'm complacently aware that there are universal requirements for properties around elemental evolution, as evolution requires that everything cease -- which would eventually include the oldest-first Protons decaying -- but still maintain that Mn is exponentially more unstable than expected for its atomic number.

Per the paper, religious-philosophical-mathematical-theoretical symmetry evolves towards experimental-observational-scientific-reality assymetry for all science branches based on recent physics and understandings that anything symmetrical is entirely incorrect at all physical levels including the most fundamental per spontaneous symmetry breaking. 

Sadly, as well for me as I'm also a trained fine art painter and historian, symmetry is a belief and a dream not a fact or a reality.

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