Tao: Symmetry and regularity (18-columns)

[Rene]

Dear John, Julio, Valery

I’ve listed below some notes about the place of symmetry and regularity in the design of the periodic table, and a suggested periodic table to this end.

René

Symmetry

While writing about this in Tao chapter 7, I was reminded of Eric’s once allegiance (in 2006) to this kind of table:

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=20

I was not a fan due the disruption of the left to right trend of metals to nonmetals. And starting with Groups 17 and 18 on the left was bizarre.

Anyway, I was prompted to look up a two-year old post to our Google group about the smoothness of periodic trends going down group 14 as C-Si-Ge-Sn-Pb versus group 4 as C-Si-Ti-Zr-Hf. Based on 38 physiochemical property z-plots, the average smoothness of trendlines going down C-Si-Ti-Zr-Hf was 1.3% better.

Now, I already knew that B-Al-Sc-Y-La was a smoother plot than B-Al-Ga-In-Tl, as the old chemists knew.

So, there was the solution to Eric’s ambition (image attached).

Period zero

I've added the electron and the neutron to period 0 so as to achieve a consistent recurrence of period lengths. Proposals to add the electron and neutron to the periodic table have a long and recurring history. I discuss this in Tao chapter 7B.

Four types of symmetry

Four kinds of symmetry are present:

• bilateral;
• four block types in each half;
• metals and nonmetals in each half; and
• a subatomic particle in each half.

Barium and the lanthanides

As you can see, I’ve added Ba to the front of the lanthanide (La to Lu) series.

The basis for doing so is the pronounced similarities between Ba and the Ln, and the alkaline earth metals generally. Examples include:

• the lanthanides are sometimes regarded as trivalent versions of the alkaline earth metals; (Evans 1982)
• the electron configurations of lanthanide cations are similar to those of alkaline earth metal cations, as the inner f- orbitals are largely or completely unavailable for bond formation; (Choppin & Rizkalla 1994)
• the lanthanide trivalent cations are essentially spherical and present an environment very similar to alkali and alkaline earth ions towards complex formation...the standard electrode potentials for the lanthanides have similar values and are comparable with the redox potentials of alkaline earth metals; (Sastri et al. 2003)
• there is a close alloying similarity between the lanthanides and Ca, Sr and Ba; (Artini 2007)
• the divalent cations of Ba, Eu and Yb exhibit many similarities; (Gschneidner 1965)
• there is a knight’s move relationship between Ca and La; [me^]
• lanthanides are effective mimics of calcium and can stimulate or inhibit the function of calcium-binding proteins; (Brayshaw 2019)
• lanthanide cations can substitute for Ca2+ and Sr2+ cations in host materials for solid state lasers. (Ikesue 2013)

Metals and nonmetals

Hydrogen is no longer by itself on the left side of the table. Metals are on the left, right and below. Nonmetals are on the right, left and above.

Hydrogen

There remains one potential point of controversy: H fits much better over F than Li in terms of the smoothness of of physico-chemical properties going down each group. The placement of H over Li therefore relies on other subjective arguments.

• Artini C (ed.) 2017, Alloys and Intermetallic Compounds: From Modeling to Engineering, CRC Press, Boca Raton, p. 92
• Brayshaw et al. 2019, Lanthanides compete with calcium for binding to cadherins and inhibit cadherin-mediated cell adhesion, Metallomics, vol. 11, no. 5, 2019, pp. 914–924
• Choppin GR & Rizkalla EN 1994, Solution chemistry of actinides and lanthanides, Handbook on the Physics and Chemistry of Rare Earths, pp. 559–590(560)
• Evans WJ 1982, Recent advances in the low valent approach to f-element organometallic chemistry, in McCarthy GJ, Silber HB and Rhyne JJ (eds), The Rare Earths in Modern Science and Technology, vol. 3, Plenum Press, New York, pp. 61–70(62)
• Gschneidner KA 1965, in Seitz F & Turnbull D (eds), Solid State Physics, vol. 16, Academic Press, New York, p. 286
• Ikesue A, Aung YL, Lupei V 2013, Ceramic Lasers, Cambridge University Press, Cambridge, pp. 26, 28
• Sastri et al. 2003, Modern Aspects of Rare Earths and their Complexes, Elsevier, Amsterdam, pp. 377, 878

^ Knight’s move relationship between Ca and La:

• The ionic radius of Ca2+ is 114 pm; that of La3+ is 117 pm
• The similarity in sizes means La3+ will compete with Ca2+ in the human body, and usually win on account of having a higher valence for roughly the same hydrated radius
• The basicity of La2O3 is almost on par with CaO2
• Freshly prepared La2O3 added to water reacts with such vigour that it can be quenched like burnt lime (CaO)
• The electronegativity of Ca is 1.0; that of La is 1.1

[Larry T.]

Rene,

It is a good looking table. I know that you are a fan of smoothness and your philosophy is based on lumping together as many physicochemical property trends as possible. Whole 38 of them!

 I see a big problem in this approach. You treat all those trends as equally important. Missing part is what they call "statistical weight". 

"A statistical weight is an amount given to increase or decrease the importance of an item." In other words, proposed 38 physicochemical trends are not equal when it comes to their importance.

   My approach is philosophically different. I strive to minimize the number of rules of the periodic system construction, giving such disciplines as spectroscopy much more weight than "Knight's move", or triads for example. Taking only a handful of physical attributes of atoms one can come up with a system which is not perfect but very close to the empirical concoction that is known as "Periodic Table". And that is what I find to be fascinating.

Kindest Regards,

Valery "Larry"

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[Rene]

Thanks Larry for your feedback. You've prompted some deep and entertaining thought on my part.

As I understand it, there isn't a problem with statistical weight since this isn't part of the periodic law. One can, of course, apply statistical weight in order to depict periodic tables examining particular perspectives of interest. However, a word of warning: if statistical weight is applied to a particular property, then such weighting needs to be applied consistently to all elements, which may result in unexpected outcomes regarding some group arrangements.

The periodic law provides for an approximate repetition of the chemical and physical properties of the elements and their compounds when arranged in order of their atomic number. The more properties that are examined for their goodness of fit going down any particular group, the more confident we can be about the bona fides of that group arrangement.

It may be that, based on a handful of physical attributes, one can arrive at a good semblance of a periodic table. That said, the need for examining three dozen or so properties may be required in some otherwise marginal cases.

There is one potential point of controversy: H fits much better over F than Li in terms of the smoothness of physicochemical properties going down each group. The difference is about 30%. So the placement of H over Li relies on some arguably subjective arguments, which could represent a form of statistical weighting. These arguments for retaining H over Li are:

1. The periodic table serves as a foundational tool in chemistry education. Its structure is designed to be as intuitive as possible for learners. Placing H above Li, despite the nuances, provides a straightforward introduction to groups, periods, and electron configurations.
2. It aligns with the basic understanding of electron configuration, making it easier for beginners to grasp.
3. While H shares properties with both alkali metals and halogens, placing it above Li avoids obscuring its alkali metal-like behavior, which is often the first chemical property introduced in educational contexts.
4. H's tendency to lose an electron is more easily explained in the context of alkali metals, which also lose one electron to form cations. This simplifies the conceptual understanding of H's behavior in reactions.
5. Likewise, in acid-base chemistry, H's role as a proton donor (hypothetically forming H₃O⁺) aligns with the alkali metals' tendency to form positive ions (cations). This analogy simplifies the teaching of acid-base reactions and unifies the concept of cation formation.
6. H can stand in for alkali metals in typical alkali metal structures; it is also is capable of forming alloy-like hydrides, featuring metallic bonding, with some transition metals.
7. The rule of first element distinctiveness acknowledges that the first elements in many groups exhibit unique properties. Hydrogen's distinct behavior—forming both H⁺ and H⁻ ions, diatomic H₂ molecules, and varying bonding types—arguably justifies its placement as the first element of Group 1, highlighting its unique characteristics.
8. H above Li nevertheless retains a knight’s move relationship to F.

It's noteworthy that one needs to rely on arguments which mostly have at least some element of subjectivity to them, in order to maintain the bilateral symmetry of the proposed periodic table, given the appreciation of symmetry itself can be a subjective phenomenon.

That said, argument #5 is rather hard to discount given the pervasive role of acid-base chemistry.

With your help I seem to have convinced myself of the merits of the proposed table.

That said, I’d like to hear from others.

René

[Rene]

I suspect the same thing is happening on the cover of Uncle Tungsten i.e. Ba and Ra also counted as lanthanides (image attached), resulting in 17-element wide set of lanthanides and actinides.

If Sacks had known about this I expect he would’ve been amused.

René