Alternative Periodic Tables (Updated. Now with a Final Thought!)

There’s an article in the current issue of Nature Chemistry that discusses some alternative ways of depicting the periodicity of the elements. There’s the IUPAC recognized Mendeleevian periodic table that everyone knows. There’s probably 3 in eyesight of you right now, isn’t there?
mendeleev(click for larger)




But how many alternative periodic tables can you think of.  Hint: there’s A LOT.  More below the jump.

For starters, some prefer to stick the lanthanides and actinides in as part of the table as a whole, instead of just a footnote.  This is the called the Janet Form.  Note how it moves the first two families and places them all the way on the right:






Another horizontal layout that strays from the classical grid, though, is called the Pyramidal Table.  I’m not sure what further information it presents, except that you can draw a bunch of parallel diagonal lines:





Or how about a vertical one based on electron configuration.  It’s useful for quickly determining valence shell configuration for any given element, but I don’t see much use beyond that.  The author of that webpage probably begs to differ.







There’s a Rota Period based on valence of the various elements.  It is very spread out.  Do with it what you will.







Paweł Najderek has developed one that looks very Escher-esque.  (btw, if you like Escher, you’ll love this page…)  You could, in principle, add an unlimited number of new periods without major revisions to the chart – as you would for the Mendeleevian table:





Timmothy Stowe also has a condensed periodic table that is meant for physicists.  It depicts the periodicity in terms of quantum numbers.







Yeah.  Now we’re starting to think outside the boxed-in grid.  But why does the table have to read left-to-right?  Several variations have ditched the grid in lieu of the spiral.  Here are three quick hits.  First is an unexplained periodic Fractal.   Second is my personal favorite alternative view, Benfey’s Periodic Spiral.  And third is the increasingly popular Chemical Galaxy, although I find the background a bit distracting.  Aside from these 3, there are a number of periodic spirals:







3D periodic tables are also all the rage.  Second Life has one (or possibly two – I don’t know second life).  This one is pretty neat.  It’d be awesome to pick it up and hold it… but I don’t see myself using it daily.






I must say, this page has an awesome list (update: link updated here to more comprehensive list) of periodic tables.  Many more than I can link to here.  Definitely worth a perusal.  Also don’t forget the Periodic Table of Videos Phil linked to a while back.

…Then there are the bozos that make periodic tables of things other than elements.  As silly as they are, the Table of Condiments that Periodically go Bad has to be my favorite.





As interesting as it is to think of alternative ways to tie together the periodicity of the elements – and as useful as those alternatives might be… I don’t see a paradigm shift happening any time soon.  I think there’s so much inertia behind the classical Meneleevian periodic table that it’s probably here to stay.

What do you think?


Update: At the requst of commenters,  I’ll incude a few more periodic tables inexplicably left out of the original round up.

Eric Scerri just left Michelle (the author of the Nature Chemistry article) a nice note about his periodic table.  It is rather easy on the eyes – more than I can say for many alternatives – I have some problems with it.  Mainly the position of hydrogen.  From my comment below:

He notes that it (his periodic table) creates another atomic number triad with fluorine and chlorine, but I don’t see that as a compelling reason to place it in the halogen family.

Chemically, we can think of hydrogen in 3 different ways. Without the electron, it is a proton – the fundamental unit of Bronsted acids. I’d argue this is the most common (most important?) chemical use of hydrogen as a player in reaction mechanisms.

With one electron, it is the hydrogen atom – a radical. Used almost exclusively in radical chemistry. Surely an important part of synthesis, but not nearly as prevalent as a protic acid.

With two electrons, it is the hydride ion. Really only seen as metal hydrides and as an organic hydride in a select few reactions (Cannizzaro). Much less common than protic acids or radical chemistry. Important, no doubt… just uncommon. When you think of hydrogen, the hydride is not your first choice for mode of reactivity.

Placing hydrogen in the halogen family implies a mode of reactivity more like fluorine than lithium. This is certainly not the case.





The Mayan periodic table also got a request from a commenter at Reddit.  It keeps intact the electron shell pattern.  Each row in the table becomes one ring in the Mayan version – so named for it’s similarity to it’s eponymous calendar cousin.






Finally, two other periodic spin-offs: cupcakes and beer.  Mmmm.







Final thought:

In viewing all these alternative tables, one thing strikes me as fascinating.  Humans have the singular characteristic (character flaw?) of demanding a pattern in everything.  Everything.  The Power of the Pattern compels us!  How many times have you celebrated a 25th anniversary or centennial of some impersonal date (mole day!)?  We love word searches and Sudoku because out of randomness we can discern a pattern.  I’m constantly looking at random collections of things and finding order amidst the chaos.  I’ll look at the carpet pattern in the waiting room and eyes and a nose and mouth will start take shape as faces start to pop out at me.  A Beautiful Mind, Pi, The da Vinci Code, hell even parts of Stranger than Fiction.  We’re obsessed with patterns.  Units of 3 become a trinity and a triad.  Groups of 12 or multiples of 5 become seemingly statistically significant to us, even if the construct is purely human.

And yet the 2nd law of thermodynamics tells us that no pattern is indefinite.  No amount of order will stay ordered.  Is all this compusion for continuity for nothing? (even alliterations are a literary pattern!)

No.  It’s useful to find patterns in the elements – after all, chemistry is just one big (big!) pattern recognition game.  For organikers, it’s “find a nucleophile; find an electrophile.  Nucleophile attacks electrophile.  Repeat.”  Polymers is a field dedicated to patterns.  So in the end, I suppose it doesn’t really matter which specific pattern on which you construct your alternative periodic table.  As long as it demonstrates the patter you’re most concerned with, then it is your ‘perfect’ periodic table.


  1. I don’t care what you think- the periodic table of cupcakes is an invaluable resource, and far more useful to my graduate studies than the real periodic table has been.

    • I get 2 hits for Periodic Table of Cupcakes

      here and here. Both are neat, to which were you referring?

      And my ‘bozo’ comment was just in jest 🙂 I actually think they’re quite clever.

  2. Chemoptoplex says:

    I’ve always found the Beeriodic table to be pretty useful.

  3. We definitely need to spruce it up a little. It’s just been so bland for so long.

    -Eric T.

  4. What is so special about the traditional layout? Isn’t it like a stamp collection? Just a way to list the elements. Others are pretty pictures with some hints of order. Three dimensional tables are hard to follow, especially when they are shown in two dimensions. The vertical formulation, the one that is useful for quickly determining valence shell configuration for any given element, is at least useful for something.

    • What is so special about the traditional layout?

      Nothing. I’m confident there is another way to illustrate the periodicity of the elements.

      One of the benefits to Mendeleev’s version is the illustration of atomic trends. Scroll to the bottom of this link for a commentary on why the grid orientation is useful – although that commentary references an alternative layout with a controversial move placing hydrogen above and between boron and carbon.

      • Janet’s left step table is just as good at illustrating the atomic trends as Mendeleev’s. The groups are the same. Some see the problem with placement of H and He above Li and Be, but that is also an illustration of an atomic trend (that is atomic structure, since all four elements have only s-electrons). Some might argue that Mendeleev’s table is superior because it’s periods end with inert gases, but that is subjective and no one knows for sure if element 118 is inert!

        • because it’s periods end with inert gases

          and the xenon fluorides would argue with group 18’s classification as inert 🙂

  5. Over on Reddit, I was alerted to the Mayan Periodic table. It’s the Mayan Periodic table not because the Mayans developed the table, but because it is constructed similarly to the Mayan calendar.


    • I forgot to say each circle is an electron shell. Therefore, each row on the table turns into one ring.

  6. As an inorganic chemist, I need a periodic table that shows the common coordination number for elements, especially the transition metals. For instance which ones prefer 6-coordinate or 5-coordinate or 4-coordinate. When you’re choosing a metal for a study, some of them will prefer to fit into what you’re working with based on their preferred coordination number.

    If anyone has a periodic table like this PLEASE, PLEASE link it!

  7. Dear Michelle,

    Thanks for featuring my own periodic table as your best choice of alternative tables in your article in Nature Chemistry.

    The design for my table which appears in your article will be used to illustrate the front cover of my forthcoming book “Selected Papers on the Periodic Table by Eric Scerri”. You will of course be acknowledged as will the editor and the artist who came up with the design.

    Now a comment on another of your Periodic Table blogs which I seem to be unable to open for some off reason.

    You mentioned and explained the term ‘lemniscate’ periodic system. I want to just mention another such system, due to William Crookes and pictured on my already published book on the periodic table, pages 252, 253.

    Eric Scerri, The Periodic System, Its Story and Its Significance, Oxford University Press, 2007.

    I have gone into some detail about this system because Crookes claimed that he had predicted the noble gases, although he did so after the facts (after their discovery). I think it is fair to say that he could have predicted them from this system.

    eric scerri
    UCLA, Chemistry Dept.

    • … that was weird.

      The main problem I have with Scerri’s table (image here, scroll about 1/3 of the way down to “Eric Scerri’s Periodic Table”) is the position of hydrogen.

      He notes that it creates another atomic number triad with fluorine and chlorine, but I don’t see that as a compelling reason to place it in the halogen family.

      Chemically, we can think of hydrogen in 3 different ways. Without the electron, it is a proton – the fundamental unit of Bronsted acids. I’d argue this is the most common (most important?) chemical use of hydrogen as a player in reaction mechanisms.

      With one electron, it is the hydrogen atom – a radical. Used almost exclusively in radical chemistry. Surely an important part of synthesis, but not nearly as prevalent as a protic acid.

      With two electrons, it is the hydride ion. Really only seen as metal hydrides and as an organic hydride in a select few reactions (Cannizzaro). Much less common than protic acids or radical chemistry. Important, no doubt… just uncommon. When you think of hydrogen, the hydride is not your first choice for mode of reactivity.

      Placing hydrogen in the halogen family implies a mode of reactivity more like fluorine than lithium. This is certainly not the case.

      Futhermore, the Scerri table completely ignores the 1s orbital and the utility of the “left step” table for illustrating orbital shells at a glance.

      • I agree. What is so important about the atomic number triads in this time and age? Curiosities of the past? Alchemy? Since we know the structure of the atom, isn’t it more important to reflect that rather than few coincidental triads?

        It is true that Scerri table is symmetrical, however, it is symmetrical for a symmetry’s sake. It is does not reflect natural symmetry of the atom.

        On the other note, why do we call spirals and 3D periodic displays tables at all? Table has to have vertical columns and horizontal rows. In this regard, Scerri table is a real table, so are few other images in the beginning of this thread.

    • I appreciate Eric’s comments about my article. It was interesting to think about what makes scientific figures appealing to scientists – cartographers have thought a lot about this with respects to maps, chemists less so with respect to the map of the chemical world.


    Selected Papers on the Periodic Table, Imperial College Press, London (coming soon)

    The Periodic Table, Oxford University Press, 2007.

  9. Just got on the elevator, and the ilnorganic chem prof was walking out with some students. The student was holding his text book… Which had the pyramdal periodic table on it. Cool.

  10. Timely topic… make sure you read the ACIE Early View on a CRAZY essay about the periodic table. Fascinatingly inane and abstract, and not very well written in my opinion, but timely nonetheless.

    • I find this comment rather surprising cbut. Professor Eugen Schwarz is one of the world’s leading theoretical chemists. The article is admittedly translated from German but is perfectly readable nonetheless. It would be interesting to hear what objections/misgivings you have about the Angewande Chemie article. Thanks for providing a link azmanan.

      eric scerri

      P.S. Still on the periodic table there is a link to a radio show from Canadian Broadcasting Corporation at the UCLA chemistry department website. After reaching this site look for the icon for the element hydrogen and click on. You will need a fast connection. The talk lasts just short of an hour and contains interviews with John Emsley, Oliver Sacks and myself. The production quality is very high. Hopefully the content is good too.

  11. As Eric Scerri has written, about the position of Hydrogen in the periodic table, “Authors have suggested groups I, VII and even IV over the years”, and notes that Atkins & Kaesz suggest “that H should be removed from the main body of the table”.
    The Alexander Arrangement of the Elements, as it is three dimensional, is capable (especially in the newest version – in production) of showing all four of these options at once; H is physically adjacent to He, Li, and F, as well as floating over the rest of the p- & s-block groups.
    ( An earlier version of the AAE can be seen at )
    As to Larry Z.s questioning the use of ‘table’ to erroneously identify 3D versions, I agree – they are ‘arrangements’ of the elements, and can do a better job of it as well, with one more needed <a href=””dimension.
    Insofar as the history of element arrangements is concerned, Larry, the first authentic one was 3D, by de Chancourtois, seven years before Mendeleev came up with his flat ‘table’.
    Flat tables, it appears, are the ‘alternatives’.

  12. correction:

    …and can do a better job of it as well, with one more needed dimension.

    • Cool site.

      Like I mentioned in my update, I think people of good faith can disagree about which pattern they want to emulate. I accept that Scerri’s table returns to the ‘roots’ of the periodic table as organized by molecular masses. I’m ok with that. I appreciate his explanation in his J. Chem. Ed. article.

      I still think there’s way too much inertia behind the current view, but I admire the creativity and effort in designing the alternative tables – even if I sounded a bit cynical in my post 🙂

  13. If anyone is interested in a reading list on alternative periodic tables, leave me a comment at and I’ll post one — there’s a lot written out there!

  14. This is a great topic for kids working on their chemistry science fair projects. What alternative periodic tables are available? Students may want to examine the spatial arrangement of the elements so that they are easier for people to remember them.

    • Good observation – they are as much superior for introduction to the periodic table to young students and in the classroom as they are inferior for reference in the everyday chemistry workplace of the professional chemist.

      Three versions are available:

      1. A quick and easy desktop reference for fun, gifts, and prizes,

      2. a hands-on take-home arrangement for student data entry and manipulation in the classroom, and

      3. a major classroom display of the 3D concept.

  15. eric scerri says:

    Let me just try to explain why I think triads are fundamental.

    First of all, this is not just a throwback to the origins of the periodic table or an attempt to base things on mass as somebody remarked.

    I am talking about atomic number triads. The relevance of this is that atomic number is the one essential criterion for identifying an element. My view is based on the distinction between an element as a basic substance (the terminology is a little unfortunate) as opposed to an element as a simple substance. For example, diamond and graphite as examples of C as simple substances which can be isolated and have properties. But the periodic table, as Mendeleev repeatedly stressed is a classification primarily of the more abstract sense of element as basic substance. The only property, or better the only characteristic of this sense of ‘element’ is its atomic number. That’s why I consider atomic number triads as fundamental, since they deal with THE essential characteristic of elements. All chemical properties such as the acidicty of H+ the fact that hydrogen forms H- ions etc are beside the point when trying to objectively settle the position of an element such as H or He which present the two biggest challenges. These ideas are explored in greater depth in my OUP book, The Periodic Table, Its Story and Its Significance.

    As a final example, the periodic table does not feature sodium or chlorine as simple substances, namely a dull silvery solid or a green gas but as abstract elements which are bonded. It is about the abstract element. The modern tendency of speaking about the PT as a classification of atoms has thoroughly confused this point.

    Please also see my recent article in International Journal of Quantum Chemistry.

    eric scerri

    • eric scerri says:

      One more point for the time being on elements as basic substances.

      It is only in this sense of the element helium that one can contemplate placing it the alkaline earths as is done in the left-step table.

      It is by ignoring its chemical properties in favor of its essential characteristics as a basic substance. As a basic substance it has no ‘properties’ as such and so does not conflict with the alkaline earth elements.

      In my book I actually recommended the lefts-step table but have subsequently changed my mind because moving He to the alkaline earths as done in the left-step table destroys a perfectly good atomic number triad consisting of He Ne Ar.

      eric scerri

      • I respect your position. In reading back over my original post and some subsequent comments, I realize I may have unintentionally sounded flippant or dismissive. I was trying to have some fun with the tables, and probably missed the mark. My apologies 🙂

        It is by ignoring its chemical properties

        Again, I respect the stance you’re taking. But, imho, this is why I look at the periodic table. I can predict the reactivity of some of the elements (some) based on other family members. This is why I disfavor spiral or vertical or the Najderek table. Too confusing to quickly discern properties.

        It is for this reason I don’t agree with moving hydrogen to The Family Formerly Known as Group 17. As I mentioned in my update, I get that the periodic table is a tool for organizing the elements based on a pattern. I don’t think moving hydrogen improves the pattern, imho.

        I highly encourage other readers to read the article I linked to earlier, as well as the webpage I linked to earlier. I haven’t read his book, but encourage readers to do so and form their own opinion 🙂

        • azmanam wrore: This is why I disfavor spiral or vertical or the Najderek table.

          May be you feel that way because you are used to a certain format? Try to use others.

      • I agree with evry point that Dr. Scerri made above except the last one. Electrons are as important part of an abstract elemnt as nucleui. Atomic number indicates not only number of protons, but number of electrons. That is why I believe that essential characteristic of He, as abstract element, is the fact that it has two s-electrons in ground state. Therefore, it should be with alkaline earths, even if it is done at the cost of destroying atomic number triad.

        • with all respect Larry, an element is characterized just by Z. The number of electrons is variable for any particular element as I am sure you are aware.

          This may seem paradoxical given that so much of chemistry is about the exchange, sharing, or transfer of electrons but in order to IDENTIFY and element one must choose an atomic property that does not change under normal chemical conditions. That property is the number of protons and nothing else.

          eric scerri

  16. Well, in this case, what if try to create a table that is based strictly on atomic number Z and the atomic number triads, why wouldn’t we list elemets like this:

    H He Li Be
    B C N O
    F Ne Na Mg
    Al Si P S
    Cl Ar K Ca
    … … … …

    Coresponding to Atomic Numbers Z:

    1 2 3 4
    5 6 7 8
    9 10 11 12
    13 14 15 16
    17 18 19 20
    … … … …

    As you can see, all atomic numbers are in perfect order and any of three elements form a perfect atomic number triad vertically and horizontally!
    Isn’t it a Perfect Layout? No need for periods of different length, no need for spdf blocks. We could make it as wide and as tall as we want (say 8 elements wide and 15 elements tall) and atomic number triads would always be there, in both direction!

    I think there is something besides Atomic number and the triads that characterizes the elements. Perhaps the abstract elements should have electron orbitals filled with electrons. Perhaps Charles Janet was right and that something is the quantum numbers, as well as “n+l”?

    • Clarification:
      It is true that an element is characterized just by Z. Continuity in regard to atomic numbers Z is necessary condition for a periodic table. However,to make a periodic table useful, other characteristics of atoms are required. Therefore, I understand the term “basic substances” as “abstract neutral atoms in ground state, with number of electrons corresponding to Z.” I also believe that Atomic Number Triads should not be considered for positioning of the elements in Periodic Table and that is why I feel this way:
      Another example of the table that is built in accordance with Z and the triads only (in better format):
      H He Li Be B C
      N O F Ne Na Mg
      Al Si P S Cl Ar
      K Ca Sc Ti V Cr
      Mn Fe Co Ni Cu Zn …. The atomic numbers and the atomic number triads are strictly followed. Is this table useful?

    • Of course you are right. In stressing the fundamental importance of atomic number I was going too far!

      Yes triads become nonsensical if one just concentrates on atomic number.

      Yes the whole point about triads, as I tried to say in my book, is that they represent a combination of chemical properties as well as numerical properties and that they gave the first hints of some underlying order to the periodic system.

      But I was not denying the importance of ‘chemical properties’ in putting together a periodic table. That would be the height of folly. I was objecting to the notion that atomic number is connected to number of electrons.

      I wonder whether Larry Z might be none other than Philip Stewart? You dont have to answer that Philip.

      I would also like to know what Larry Z means by “…the quantum numbers as well as n+l”

      eric scerri

      P.S. Another pitch for the radio show which is on the PT and posted at the UCLA website. I mentioned this somewhere above but the ordering of postings is a little odd on this website.

      Go to

      then look for the icon for H (hydrogen) and click on from there. Its a one hour radio show from Canada, featuring John Emsley, Oliver sacks and yours truly.

      • Eric,

        I would like to assure you that I am not Philip Stewart. I am familiar with his Chemical Galaxy and his latest article in Foundations of Chemistry about Janet. I’m a fan of Janet’s Left Step PT. I believe that it is the most notable alternative. Its groups are identical to those of traditional PT but follow order of quantum number l=3,2,1,0 (that is fdps) instead of l=0,3,2,1, that is sfdp in traditional PT. It retains continuity in regard to Z and its rows correspond to n+l.
        According to your book (that I like very much) you also used to be LSPT’s fan.

        • Correction. LSPT’s groups are identical to those of traditional PT with exception of helium. Sorry, but I have to say that idea of using atomic number triads as another justification for placing H above Cl and He above Ne is far-fetched one.

          • eric scerri says:

            The reason why I ‘jumped ship’ regarding the left-step table in spite of it’s wondrous formal beauty and elegance is partly that too many chemists I consulted and too many people at talks I give on the periodic table refuse to buy ‘He as an alkaline earth element’.

            The best argument I could find when I wrote my book was one based on elements as ‘basic substances’ which have no manifest properties, in which case the obvious objection regarding He being very unlike the alkaline earths could be ignored.

            But I now think this is a rather weak argument. It is of the form of a “why not” put He in the alkaline earths type argument rather than a positive reason why one SHOULD place it there, other than the formal elegance of the l.s.t.

            On the other hand my argument for doing the reverse in a sense (moving H across to group 17 rather than He to group 2, is based on a positive argument. because it preserves a perfectly good triad in He, Ne, Ar while also providing a new one in H, F, Cl. It is also based on the ONLY ‘peoperty’ which can be assigned to an element as a basic substance, namely atomic number.

            Why should the fact that elements fall into triads work for all periods except the very first short period of 2 elements? I dont think any periods should be excluded. I like a little more democracy in my periodic table.

            There is a letter to the editor of Journal of Chemical Education, from Mike Laing, and a response from me due to appear in a/the next issue of the journal which takes up this whole question of atomic number triads.

            Returning to whether they are fundamental or merely accidental, I also argue that atomic number is a fundamental property of the nucleus that ultimately governs the behavior of electrons and hence the chemistry of the elements.

            This idea is controversial but a number of studies are reaching the same conclusion. For example, Bonchev has argued that there are very good correlations between electronic and nuclear structure (references provided on request). Also a number of authors claim the the origin of the preference for L-amino acids etc. in nature can be traced to parity violation in the weak nuclear force. There is also a paper in a recent Foundations of Chemistry issue by Richard Pagni on this topic.

            Larry, would you consider identifying yourself to me directly in an E-mail if you wish to remain anonymous in this forum?


          • I’m going to have to call into doubt a correlation between nuclear structure and electronic configuration. I could strip all the electrons off of Uranium and it will still have the same half-life as if it had all its electrons.

          • sorry but this would be going in the opposite direction and claiming an influence of electronic structure on the nucleus.

            I am pointing to the possible opposite causal process. The nucleus, which is surely at the more fundamental level, may influence electronic structure.

            What you are alluding to is ‘downward causation’ and I agree with you it’s unlikely. It would be like suggesting that biology influences microphysics or some such thing.

            It has been discussed in philosophy of science but it’s not what I am discussing here.

            eric scerri

          • Oh, that would be more probable. But since the protons are so far removed from the electrons, I still would find it hard to believe that electrons are that sensitive to nuclear structures and nuclear shells.

          • Can you be a little more specific? So far away relative to what? I am talking weak nuclear force here not strong. Why is the former so implausible?

            eric scerri

          • Sorry, I was thinking about the strong force. Since s-electrons can spend some of their time in the nucleus I guess it can be possible.

          • Eric Scerri wrote:
            “The nucleus, which is surely at the more fundamental level, may influence electronic structure.”

            I tend to agree with Eric. I believe that there is certainly some, currently unknown, reciprocity when it comes to electronic and nuclear structure and the reason for my belief is that the famous magic numbers that Maria Goeppert-Mayer got her Nobel Prize for: 2,8,20,28,50,82,126… and Chemistry’s magic numbers 2,2,8,8,18,18,32,32 (Janet’s layout) can be mathematically arrived via tetrahedral sphere stacking as presented at . Call it fringe or else, but I think that this mathematical exercise is far more interesting than the atomic triad idea.

            Eric, you might be negatively surprised, but I, “Larry Z.”, is the author of that site.

          • Thanks Larry Z. In that case we have had some previous correspondence although I am afraid that I cannot recall what course it took.

            There are so many people working on the periodic table these days that it is becoming difficult to keep track of who everybody is. Hopefully I did not say anything to impulsive about your work and will print out your website again now to refresh my memory.

            eric scerri

          • OK, I have read your material again.

            Let me get this right. You place both H and He in two positions, H in groups 1 and 17, He in 2 and 18 (a la IUPAC). I am not interested so much in shape of a system as you know but which groups elements are placed it.

            Now please explain why just 2 elements out of 120 have the distinction/freedom to belong to two groups?

            I note that you stress the preservation of the H,F,Cl and also He,Ne, Ar triads as a good feature and am wondering whether you were influenced in this by my papers, since nobody else seems to think that there is any validity in maximizing atomic number triads?

            Philip Stewart has told me a couple of times that he likes your table but I dont understand why he/you see it as an improvement on Janet’s format. At least Janet commits himself to one place for H and He whereas you do not.

            eric scerri

          • I would also like more information on how your arrangement gives a better account of the relationship between quantum numbers than according to traditional wisdom. Or am I attributing something to you that you do not actually claim?

            eric scerri

          • Thanks, Eric.

            Yes, in the beginning I was influenced by your papers and mentioned atomic number triads in my correspondence with Mark Leach who took parts of my email (with my permission, of course) and displayed it on his meta-synthesis web site. However, the more I have been thinking about the triads, the less interested I’ve become. The only reason for keeping H and He in two locations was an attempt to please too many people at the same time (which is probably wrong thing to do).
            The periodic table can be built 1)on a basis of properties of the elements or, 2)on a basis of atomic structure. I tried to address both cases.
            But if it is built strictly on a basis of atomic structure, H and He firmly belong with alkali metals and alkaline earths respectively. I think that no one can dispute that. The tetrahedron theory is dealing strictly with atomic structure.
            Philip Stewart, Henry Bent and many others (including Roald Hoffmann who sent me a short email saying that he likes my table), think that ADOMAH PT is an improvement to Janet because shifting blocks by the value of the quantum number “l” has allowed direct readout of the primary quantum number “n”, that no other PT formulation has ever allowed. This shift, as mentioned by azmanam above, made the ADOMAH PT useful for determining valence shell configuration for any given element quickly. This might appear to be a minor improvement, but this feature also serves as a proof that ADOMAH PT is truly based on electronic structure of atoms and is indeed the strictly objective formulation. (Please, note that this is true only when H and He are located next to Li and Be, and not with F and Ne). No other periodic table formulation allows direct and simple derivation of the electron configurations of the atoms. If you know one, please let me know.
            Then it was realized that f,d,p,s blocks represent consecutive slices of the regular tetrahedron and aufbau process can be modeled via expanding tetrahedron of equal spheres.
            Please, give an hour of your time and read it all. I do not expect you to agree with every statement on that web site , but, quoting Henry Bent, it is “scientifically solid”. Please, do not hesitate to contact me with any questions.

          • I just realized that I did not answer Eric’s question: “I would also like more information on how your arrangement gives a better account of the relationship between quantum numbers than according to traditional wisdom. Or am I attributing something to you that you do not actually claim?”.

            Yes, I do claim that tetrahedral sphere arrangement gives better account of the relationship between the quantum numbers, specifically, between “n” and “l”. Currently, quantum number “l” is defined as l=0,1,2…, n-1. The tetrahedral arrangement point to more complex relationship between “n” and “l”. If you look at typical mnemonic diagram of Aufbau process, you will see that the elements located at the bottom right corner are shaded or crossed out. Typically, there is a note stating that there are no existing elements that correspond to that (shaded) part of the mnemonic. Actually, I determined that this happens because of oversimplified definition of “l”. Indeed, if, for example, n=7, you will not find existing elements in the current periodic table corresponding to l=(7-1) or (7-2). The reason for that becomes clear if aufbau process is modeled as tetrahedral stacking of spheres as shown on my web site. Formulae 9 and 9a, as well as 10 acurately depict the actual relationship between “n” and “l”.

          • sorry this is not clear. please explain

            this happens because of oversimplified definition of “l”. Indeed, if, for example, n=7, you will not find existing elements in the current periodic table corresponding to l=(7-1) or (7-2).

          • The relationship between quantum numbers n and l which you claim to be defective is derived from first principles of quantum mechanics and has applications in many areas of atomic physics.

            If you claim it is incorrect you will need to give a theoretical argument against it rather than one from your tetrahedral model which as far as I can see lacks and theoretical justification.

            I think I now see what you mean about the lack of existence of l = 7-1 or 7-2. I assume you are referring to the fact that no element has yet been synthesized which has electrons in h or i orbitals?

            I suppose you could also have pointed to the lack of elements for which l = 6-1, namely h orbitals.

            Why not also claim that there are presently no elements with n-1 = 4 or g orbitals. Perhaps because you realize that the technology for synthesizing superheavy elements is close to the point of making an element with g electrons?

            eric scerri

          • Yes, I could point to l=6-1 and l=5-1. It does not matter. If those elements are ever synthesized they would push tetrahedral envelope to edges E=12 and E=10 respectively. Today’s table fits entirely in tetrahedral envelope with E=9. You see, if we would live on a hypothetical planet where only fisrt 20 elements known, we would think that there are no elements corresponding to l=3-1 (E=6) or l=4-1 (E=8). Introduction of new n+l level pushes tetrahedral envelope limits.
            Yes, I am convinced that definition of “l” is defective simply because lmax=n-1 is not sufficient to describe relationship between “n” and “l”. Misterious n+l rule that was found in 1930’s was necessary to correct the deficiency and to pinpoint the true relationship. Formulae 9 and 9A, or 10 combine n-1 with n+l, at least on electron level, but perhaps on nuclear level too.

          • In addition to my previous post I’d like to state following:
            The three quantum numbers n, l and ml are generated by applying boundary condition to solutions of the Schroedinger equation, and arise form Radial Function, the angular Wave Functions respectively and Indeed, the solutions for n=7 and l=6 as well for n=5 and l=4 do exists, but the problem is that the current periodic table is confined to n+l level of 8, corresponding to the tetrahedron with edge E=9. What I am trying to say is that if you plot sequence l=0,1,2…n-1 in n, l coordinates you will get a straight line that begins at n=1, l=0 and continues at 45 degrees to infinity. But in reality, because of n+l rule, it is not continuous line, but a broken line that peaks approximately at l=(n max)/2 and returns to l=0, n=n max (and this is a physical fact). So, this n+l =E-1 is another boundary, that, I believe, has connection to the uncertainty principle.

          • eric scerri says:

            Thanks but this is still not clear to me.

            The relationship between n and l is derived form first principles and deals with all of atomic physics not just the form of the periodic table.

            If the relationship is wrong for the PT it is also wrong in general. Are you claiming this? If so why has this never been noticed before?

            And you are not providing experimental evidence for its breakdown just an argument based n your tetrahedron.

            eric scerri

          • You are right, more work has to be done. This is not completely theoretical stuff though. As I mentioned above, definition of “l” as l=0,1,2,…, n-1 does not reflect relationship between “n” and “l” completely since obscure n+l rule, that was empirically derived, had to be introduced in order to improve our understanding of that relationship. I believe that n+l, that appears in radial wave function, should be viewed in combination with n-1. I think that it is quite remarkable that the tetrahedral sphere packing mimics the periodicity so closely and accounts for the period lengths (2,2,8,8,18,18,32,32…), the size of the electron shells (2,8,18,32,32,18,8,2), as well as the nuclear magic numbers (2,8,20,28,50,82,126…) at the same time. I might not be able to explain everything. After all, Kepler’s interest in geometric patterns led to Newton’s theory of universal gravitation. I feel that it is my duty to share with others my findings in regard to the geometric patterns that mimic the phenomenon of the periodicity of the atomic structure so closely. I just hope that my work is useful and that one day my findings will be explained and it does not really matter who would complete the explanation. Thank you, Eric, for your interest, questions and comments and many thanks to azmanam for starting this thread and noticing the usefulness of my periodic table that you called “the vertical one”.

            Valery Tsimmerman, a.k.a. Larry Z.

          • eric scerri says:

            I had not realized that you were also claiming to account for nuclear magic numbers. Can you explain how that happens with your tetrahedron?

            eric scerri

          • Thanks. I will look again.

            Can you provide a reference to the work of Garai please?

            eric scerri

          • I have just noticed that the link to Garai article shown on my web site is no longer working. It was working before. Through the google I found even earlier article by J.Dudek dating back to 2002: Try this link, it works.

            I have a paper copy of the article:
            “The double tetrahedron structure of the nucleus” by J. Garai, Department of Earth Sciences. Florida International University. dated 10/04/03.

            I thought about your earlier question why deficiency of “l” have not been noticed before, especially in nuclear physics, for example. I think that it happens because definition of “l” as l=0,1,2,3,…,n-1 is not completely wrong. It is simply incomplete as indicated by the existence of n+l rule. n+l rule became evident thanks to the spectroscopy. But we do not have such precise methods to probe the structure of the nucleus. Discovery of nuclear n+l rule would be possible only when we improve precision of the methods of probing the atomic nuclei. At this point we have two theories: Liquid Drop and Shell and we are not even sure what the nucleus is like: liquid-like, solid-like or crystal-like?

          • Thanks very much Larry, especially for the ref’ to Dudek’s paper.

            This is becoming very interesting.

            Just as a matter of interest, did you ‘rediscover’ your tetrahedral symmetry idea or did you first see the papers by Garai and Dudek?

            eric scerri

          • The Garai paper that you mention?

            Is it published in a journal?
            If so please give full reference.

            eric scerri

          • Eric,

            I found Garai’s paper at in fall of 2007, but this link does not work anymore. The paper copy that I have does not mention any journal name.

            To answer your previous question I will give you a chronology of my work on ADOMAH PT and the Tetrahedron, I have it all documented:

            On 11/29/05 I desided to cut LSPT’s length in half by placing elements in rectangular cells instead of squares. I was very surprized when I noticed that the fdps blocks have the same perimeter of 18 units. I coudn’t understand why.
            On 02/13/06 I realized that, if f,d,p blocks are shifted vertically by amount of “l”, the rows would correspond to the quantum number “n”. Similarly, if blocks are shifted horizontally, “ml” values would also line up. I realized that I am looking at some 3D shape, but I did not know what it was. On February 5, 2009 I contacted Mark Leach and he published ADOMAH PT on his meta-synthesis web site. It is there since. In early fall of 2007 I felt that I need to learn more about the structure of the nucleus. I went to Wikipedia’s article on nuclei and there was a link to X.Borg’s article about possible double tetrahedron structure of the nucleus at Regretably, this link does not now work either. There, X. Borg wrote how to “reverse engineer” the magic numbers using the tetrahedral sphere packing. There, he referred to the Garai’s article mentioned above. I went to the arxiv site and downloaded that article. In that article he was discussing the nucleus and the Pyramidal PT, but I felt that my version of LSPT would work even better. I went to Michael’s store and bought Christmas decorations that had red and green spheres. I cut them out and started to assemble the tetrahedron using red and green spheres. On 10/01/2007 I assembled my first red and green tetrahedron of 60 spheres corresponding to 120 elements. While I was doing that I realized why f,d,p,s blocks have the same perimeter and why “n” and “ml” line up. I also realized why the areas of the tetrahedron slices are the same as those of modified LSPT that I called it ADOMAH PT.
            That what happened.

            V.”Larry” Tsimmerman

          • Correction to the above post. My tetrahedron consists of 60 red and 60 green spheres. Total of 120 spheres. Each red sphere corresponds to couple of elements (ms=+1/2,-1/2). Also, the link to Garai’s paper is working again: You can download Garai’s article in PDF format from there.

            V.”Larry” Tsimmerman

            P.S. I haven’t seen Dudek’s paper until yesterday, when I googled in order to find reference to the Garai’s article for you. I am studying it now.

          • OOPS. Another error.
            ADOMAH PT was first published at in February of 2007, not 2009.
            Also, X. Borg’s web site:

  17. I’m still looking for a periodic table that shows the common coordination numbers for transition metals (for instance Fe likes 6-coordinate, Cu likes 5-coordinate, etc.) If anyone has seen one please post a link! You will make my life so much easier!

  18. Pingback: Chemistry Blog » Blog Archive » My Attempt At a Periodic Table

  19. I show tables like this in a recent article in International Journal for Quantum Chemistry. Somebody more Net Savvy than me could perhaps post the link for it. Alternatively Bob please contact me by regular E-mail and I will send you a pdf copy.

    eric scerri

  20. eric scerri says:

    Thanks very much mitch

    eric scerri

  21. I would like to start a new thread related to the Periodic Table.

    The manner in which electron shells fill is governed by the empirical rule of n + l rather than an n rule.

    I claim that the n + l rule has not yet been deduced from quantum mechanics and as a consequence the periodic table has not been fully explained.

    The usually encountered textbook accounts of the periodic table imply that QM explains everything.

    Any comments folks?

    eric scerri “The Periodic Table, Its Story and Its Significance, OUP, 2007.

    • Eric, I agree with you. n+l rule has not been deduced from quantum mechanics. I have stated my position in this regard in my postings above. I think that you will not be able to find enough people interested in this topic in order to justify a new thread. After all it is convenient to think that QM, in its current state, explains everything, but that is not so.

  22. Response to original comment,

    Update: At the requst of commenters, I’ll incude a few more periodic tables inexplicably left out of the original round up.

    Eric Scerri just left Michelle (the author of the Nature Chemistry article) a nice note about his periodic table. It is rather easy on the eyes – more than I can say for many alternatives – I have some problems with it. Mainly the position of hydrogen. From my comment below:

    He notes that it (his periodic table) creates another atomic number triad with fluorine and chlorine, but I don’t see that as a compelling reason to place it in the halogen family.

    Chemically, we can think of hydrogen in 3 different ways. Without the electron, it is a proton – the fundamental unit of Bronsted acids. I’d argue this is the most common (most important?) chemical use of hydrogen as a player in reaction mechanisms.

    With one electron, it is the hydrogen atom – a radical. Used almost exclusively in radical chemistry. Surely an important part of synthesis, but not nearly as prevalent as a protic acid.

    With two electrons, it is the hydride ion. Really only seen as metal hydrides and as an organic hydride in a select few reactions (Cannizzaro). Much less common than protic acids or radical chemistry. Important, no doubt… just uncommon. When you think of hydrogen, the hydride is not your first choice for mode of reactivity.

    Placing hydrogen in the halogen family implies a mode of reactivity more like fluorine than lithium. This is certainly not the case.


    Thanks for the comment but my placement of hydrogen is not based upon its obvious chemical reactions, otherwise placement in the halogens would indeed seem a little contrived.

    The idea is to place the element as a ‘basic substance’ rather than as a simple substance. There has been a great deal of discussion on this topic in the philosophy of chemistry literature.

    Mendeleev himself stressed that the periodic table was primarily a classification of the abstract elements not their properties as simple substances or as isolated elements. The periodic table is as much a classification of elements as they occur in compounds.

    Elements as basic substances are not directly accessible to experimental data. Their characteristics must be inferred. Mendeleev did this by considering bonded elements as well as the isolated elements.

    Some 50 years later, the characteristic of elements as basic substances was recognized as being atomic number by Fritz Paneth a prominent radiochemist who also provided the official IUPAC defninition for what constitutes an element and which stands to this day. An element is picked out by citing its atomic weight. This is a necessary and sufficient criterion.

    When I proposed my periodic table with H in the halogens I was arguing in terms of atomic number triads. H, F and Cl form a new atomic number triad if H is placed in the halogens but not if it is left in its traditional place in group 1.

    I claim that this placement is more fundamental than appealing to properties of H as a simple substance or even as a bonded element since it comes closest to the notion of element as basic or abstract substance since it deals with relationships between atomic numbers, the one criterion for defining elements as basic substances.

    References to the literature available on request.

    Here is one of the papers,

    E. Scerri The Dual Sense of the Term “Element, Attempts to Derive the Madelung Rule and the Optimal Form of the Periodic Table, if any, International Journal of Quantum Chemistry, (2009), 109, 959-971.

    eric scerri

  23. Pingback: Alternatieve Periodieken « Scheikundejongens

  24. jess tauber says:

    Hi- I came up with the same tetrahedral arrangement of the periodic table as Larry Z. some 30 years ago, even showed it at a local meeting of the American Chemical Society, where it was met with yawns and worse. Larry’s work was completely independent, so far as I can tell. The most interesting thing is the ‘perimeter’ effect, as he has written- that is if you look at solid blocks of s, p, d, and f orbitals, and count only electron pairs, you always get a sum of 9. That is, S is, in this scenario, 8 deep and 1 pair across, P gives you 6 deep vs. 3 pairs across, D 4 deep and 5 pairs across, and then finally F is 2 deep and 7 pairs across.

    In the actual depiction with balls only 60 give you the pairs of electrons, leading me to suspect that perhaps one can split the system up and start building up the tetrahedron from two ends, on legs perpendicular but not connected by any vertex. If you do this then all 120 balls are used, and there is no dead space in the figure.

    In this kind of system element 120 is ‘the end’- no other elements are possible if the sum 9 relation fixes things. In any case nuclear forces stop helping by element 120 anyway, science fiction elements notwithstanding.

    I suspect that there are other geometrical patternings that can be found within the figure when unusual elemental, ionic, or molecular properties are taken into account, or interactions with nuclear structure. Nature is nothing if it isn’t math-crazy.

    See: >

    Jess Tauber

  25. Just to let people at this forum know, Jess have contacted me on June 12, 2009 at 12:18 am via email. Next day, June 13 he emailed me a link to a forum where he described (with words) that if s,p,d,f blocks are separated and shrank in half, they could be presented as slices of the tetrahedron. This is about 6.5 years before I have come up with the same idea. We agreed to collaborate in the future and keep regular email contacts.

    Despite the idea of the tetrahedron, there was also a difference in our approach. Jess was happy to find out that if s,p,d,f blocks are separated, they could be presented in 3D as the tetrahedron. I tried to keep them connected and used the tie lines for that purpose, in order to preserve the continuity in regard to the Atomic Number Z. This has become known as ADOMAH Periodic Table. I tried to keep blocks connected also in 3D by using concept of the tetrahedral packing of spheres that led me 3D representation of the Aufbau process.

    Earlier, I was also contacted by George Jelliss (UK), who also arranged the blocks similar to the ADOMAH PT in 1986, however, his representation also lacked the continuity in regard to Z.

    In any case, all this points to one thing: The tetrahedral representation of the periodic system is objective and, therefore, superior to all other (subjective) representations ofthe periodic law.

    Sorry, but I have to disagree with the author of the “Final Thought” above. There is the Perfect representation of the Periodic System indeed and it is presented at

    Valery Tsimmerman (Larry Z.).

  26. What do you think about my Periodic Table? Click my name to see it.

  27. Nice periodic table except Lu and Lr should be placed underneath Sc and Y in group 3.

    See the recent articles and letters to the editor about this issue in the October issue of Journal of Chemical Education.

    eric scerri

  28. This is my spiral table. The Periods are included but it is governed more by the groups which I believe is more useful. The other aim of this table is to break away from only using the element symbols. Yes, yes I know they are well accepted but I believe this opens chemistry up to a larger audience. Thinking of doing another table with the same design but using the colours to define each category. It would lose its simple elegance but may be more useful. Feedback welcome!

  29. Pingback: ELPC G2 connections for Assignment 3 « Becoming Miss Colley

  30. Marco Piazzalunga says:

    Hi, I’m Marco Piazzalunga, I’m twelve, I’m from Bergamo, in Italy. I’ve made an alternative periodic table based on a circular model, I hope you enjoy it.

    Periodic table’s link:

  31. i want to know alternative chemical used in place of any chemical having same application

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  33. Here is a fun interactive one to include. Thanks for this blog post!

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  37. Pingback: Periodically Thinking About the Period Table – Kyle’s Blog

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