Periodic spiral of the elements (Peña & Guerra 2024)
Rene
- Periods 2 to 5 are shown but it’s not apparent what period H belongs to.
- The location of groups 11 and 12 around the corner from group 10 is quite clever.
- Referring to groups 11 and 12 as noble metals is daft.
- I’m not so sure about the positioning of group 2. There does not seem to be a good reason as to why it partially occupies the east face of the spiral rather than is south face.
- The f-block occupies six cells on the east side and eight on the north side. Since the f-block metals are known to show double periodicity it would be apt to show seven of them on each of the two sides.
mavorte1
"The spiral is effectively a 3D representation that is equally legible in 2D."
1. “Periods 2 to 5 are shown but it’s not apparent what period H belongs to.”
REPLY: Since Period 2 is labeled and hydrogen appears before the Period Divide line, it logically belongs to the previous Period 1.
3. “Referring to groups 11 and 12 as noble metals is daft.”
REPLY: To my knowledge, there’s no collective name for the metals in Groups 11 and 12 that have the tendency to use s orbitals instead of d orbitals. Rather than inventing a new term, I chose to reuse the familiar (albeit vaguely defined) name “noble metals” and assign it a functional meaning. Why "noble metals"?
- Many metals in these groups exhibit low reactivity and high value,
- They are positioned at the end of the d block, analogous to noble gases at the end of the p block.
This name is easy to critique, but proposing a better alternative is more difficult. Regardless, this naming choice does not impact the validity of the representation, and should a better term gain consensus, it can be easily replaced.
4. "I’m not so sure about the positioning of group 2. There does not seem to be a good reason as to why it partially occupies the east face of the spiral rather than is south face."
REPLY: Moving Group 2 southwards would:
- Shift the superactinides (g block) loop southwards, which is quite inconvenient
- Lose the current Groups 11 and 12 ("noble metals") cluster around the corner
- Shift the majority of the elements from the current S side to W side, weakening the visual parallel with the traditional periodic table
Also, I find the SE corner to be a suitable position for the Period Divide line. I encourage you to sketch your proposed change and check these potential problems. I tried many alternatives before arriving at this current proposal.
5. "The f-block occupies six cells on the east side and eight on the north side. Since the f-block metals are known to show double periodicity it would be apt to show seven of them on each of the two sides."
REPLY: Following up on my previous reply, I invite you to sketch your new proposed change. Moving the f-block to place seven elements on each side would separate group 3 from the rest of the d block, and group 11 would be disconnected from group 12, disrupting the "noble metal" cluster. Additionally, this arrangement would conflict with your earlier proposal, as it’s not possible to position the s block southwards while also placing seven d block elements on each side of the square.
I hope this helps clarify some aspects of this design. I’ve also attached a high-resolution image in case anyone wishes to print or publish it.
Best regards,
Mario RP
Jess Tauber
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Jess Tauber
Here's a simplified versionAnd an older version from 2008.Julio Antonio Gutiérrez Samanez
El dom., 27 jul. 2025 05:17, Julio gutierrez samanez <kut...@gmail.com> escribió:Hello, distinguished colleagues. I've just seen the "square spiral." It's certainly a new endeavor, but it's very much under the straitjacket of Chemistry and its insurmountable groups and blocks. In reality, I see it as forcing the standard table into a square.
Whether square or circular, a spiral must be a continuous line. A radius vector that grows in size as it rotates through a certain angle, like the Archimedean spiral, with one restriction: this angle, for every two circumvolutions or periods with the same number of elements, is what we call a binode or dyad (according to Baca Mendoza and Charles Janet).
The division pattern is the one proposed by Pauli: 2n^2 = 2, 8, 18, 32, 50, 72... where n is valid for two periods that change as a new azimuthal quantum increases. That is, for n = 1, the background will be formed by two nested circles (for example, of radius 1 and radius 2), for two spirals. Since 2n^2 = 2, then this background is divided into two radii or a diameter, making two crescents. If the two spirals are inscribed, only 4 elements fit at the intersections with the diameter, according to the relation 4n^2 = 4. For n = 1.
For n = 2, the background is expanded to include two "annulus" of larger radii for the second pair of periods. The division pattern will be 2 (2 ^2) = 8, and the number of elements in the two spirals will be 4(2^2) = 16, because in this binode there will be 4 s elements, as in the first, plus 12 d elements. In the following way: (6, 2; 6, 2) this is why it is said that there is a "doubling of periods," but this is only in the number of elements, since the even period develops on another level, in another, broader spiral that envelops the first. And so on.
As you can see in the following link, my allusions to Hegel and Engels raised many hackles.
Julio
https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=946
Hola ilustres colegas. Recién veo la “espiral cuadrada”, ciertamente, es una tentativa nueva, pero muy sometida a la camisa de fuerza de la Química y sus insalvables grupos y bloques. En realidad veo que es como meter por la fuerza a la tabla estandar dentro de un cuadrado.
Sea cuadrada o circular, una espiral debe ser una línea continua. Un radio vector que crece de tamaño a medida que rota en cierto ángulo, como la espiral de Arquímides, con una restricción: este ángulo, para cada dos circunvalaciones o periodos con el mismo número de elementos que llamamos bínodo o díada (según Baca Mendoza y Charles Janet).
El patrón de división es el que propuso Pauli: 2n^2= 2, 8,18, 32, 50, 72… donde n es válido para dos periodos que cambian al incrementarse un nuevo cuántico azimutal . Es decir, para n =1, el fondo será formado por dos círculos anidados (por ejemplo, de radio 1 y radio 2), para dos espirales. Como 2n^2=2, entonces este fondo se divide en dos radios o un diámetro, haciendo dos medias lunas. Si se inscribe las dos espirales, en las intersecciones con el diámetro solo caben 4 elementos, de acuerdo con la relación 4n^2 = 4. Para n =1.
Para n = 2, se amplía el fondo para dos “coronas circulares” de radios mayores para el segundo par de periodos. El patrón de división será 2 (2 ^2)= 8 y el número de elementos en las dos espirales será 4(2^2)= 16, porque en este bínodo habrá 4 elementos s, como en el primero, a los que se incrementa 12 elementos d. De la forma que sigue: (6, 2; 6, 2) por esto se dice que hay “duplicación de periodos ” pero, esto es sólo en el número de elementos, pues el periodo par se desarrolla en otro nivel, en otra espiral más amplia que envuelve a la primera. Así, sucesivamente.
Cómo se puede ver en el link siguiente que. por mis alusiones a Hegel y Engels, sacó muchas ronchas.
Julio Antonio Gutiérrez Samanez
To view this discussion visit https://groups.google.com/d/msgid/PT-L/CAO6d3h%2BHap%3DzeCsVj_woA%3D5F7x3PZd9%2Bmf6Adxr8TmbO3P7o0Q%40mail.gmail.com.
Rene
Apologies for not addressing your points earlier, at least within this group.
1. There is a lot to your periodic spiral i.e. more than meets the eye and it has consequently taken me a while to gather my thoughts, in between other commitments In my earlier comments I referred to your periodic spiral as "out of the box" thinking and that remains my impression.2. Jess and Julio: thanks very much for sharing your thoughts, which I have yet to studiously read.3. Although I am still researching the nature of the group 11 and 12 metals, I suspect they can be referred to as "incipient p-block metals", given all of them show, or are known to show, main-group chemistry. Of course, Cu and Au show transition metal chemistry too, while in its most stable +1 oxidation state, Ag shows main-group chemistry. Along the base of the periodic spiral, the labels would then be:incipient "p" block PERIOD DIVIDE"p" blockmetalsI think there may be some similar things happening in the other three corners of the periodic spiral.
mavorte1
Regarding the collective name for metals from groups 11 and 12, I find that "incipient p-block metals" may be a long and potentially misleading name, as it could suggest involvement of p orbitals, whereas the distinctive feature is actually the involvement of s orbitals. As I mentioned in my previous email, finding a new name is quite challenging. For now, I continue to support the term "noble metals" with the reframed functional interpretation, unless another term gains consensus and popularity.
Warm regards,
Mario RP
Julio gutierrez samanez
Hello, distinguished colleagues. I've just seen the "square spiral." It's certainly a new endeavor, but it's very much under the straitjacket of Chemistry and its insurmountable groups and blocks. In reality, I see it as forcing the standard table into a square.
Whether square or circular, a spiral must be a continuous line. A radius vector that grows in size as it rotates through a certain angle, like the Archimedean spiral, with one restriction: this angle, for every two circumvolutions or periods with the same number of elements, is what we call a binode or dyad (according to Baca Mendoza and Charles Janet).
The division pattern is the one proposed by Pauli: 2n^2 = 2, 8, 18, 32, 50, 72... where n is valid for two periods that change as a new azimuthal quantum increases. That is, for n = 1, the background will be formed by two nested circles (for example, of radius 1 and radius 2), for two spirals. Since 2n^2 = 2, then this background is divided into two radii or a diameter, making two crescents. If the two spirals are inscribed, only 4 elements fit at the intersections with the diameter, according to the relation 4n^2 = 4. For n = 1.
For n = 2, the background is expanded to include two "annulus" of larger radii for the second pair of periods. The division pattern will be 2 (2 ^2) = 8, and the number of elements in the two spirals will be 4(2^2) = 16, because in this binode there will be 4 s elements, as in the first, plus 12 d elements. In the following way: (6, 2; 6, 2) this is why it is said that there is a "doubling of periods," but this is only in the number of elements, since the even period develops on another level, in another, broader spiral that envelops the first. And so on.
As you can see in the following link, my allusions to Hegel and Engels raised many hackles.
Julio
https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=946
Hola ilustres colegas. Recién veo la “espiral cuadrada”, ciertamente, es una tentativa nueva, pero muy sometida a la camisa de fuerza de la Química y sus insalvables grupos y bloques. En realidad veo que es como meter por la fuerza a la tabla estandar dentro de un cuadrado.
Sea cuadrada o circular, una espiral debe ser una línea continua. Un radio vector que crece de tamaño a medida que rota en cierto ángulo, como la espiral de Arquímides, con una restricción: este ángulo, para cada dos circunvalaciones o periodos con el mismo número de elementos que llamamos bínodo o díada (según Baca Mendoza y Charles Janet).
El patrón de división es el que propuso Pauli: 2n^2= 2, 8,18, 32, 50, 72… donde n es válido para dos periodos que cambian al incrementarse un nuevo cuántico azimutal . Es decir, para n =1, el fondo será formado por dos círculos anidados (por ejemplo, de radio 1 y radio 2), para dos espirales. Como 2n^2=2, entonces este fondo se divide en dos radios o un diámetro, haciendo dos medias lunas. Si se inscribe las dos espirales, en las intersecciones con el diámetro solo caben 4 elementos, de acuerdo con la relación 4n^2 = 4. Para n =1.
Para n = 2, se amplía el fondo para dos “coronas circulares” de radios mayores para el segundo par de periodos. El patrón de división será 2 (2 ^2)= 8 y el número de elementos en las dos espirales será 4(2^2)= 16, porque en este bínodo habrá 4 elementos s, como en el primero, a los que se incrementa 12 elementos d. De la forma que sigue: (6, 2; 6, 2) por esto se dice que hay “duplicación de periodos ” pero, esto es sólo en el número de elementos, pues el periodo par se desarrolla en otro nivel, en otra espiral más amplia que envuelve a la primera. Así, sucesivamente.
Cómo se puede ver en el link siguiente que. por mis alusiones a Hegel y Engels, sacó muchas ronchas.
To view this discussion visit https://groups.google.com/d/msgid/PT-L/CAO6d3h%2BHap%3DzeCsVj_woA%3D5F7x3PZd9%2Bmf6Adxr8TmbO3P7o0Q%40mail.gmail.com.
Julio gutierrez samanez
Mario Rodriguez
I’d like to clarify some comments regarding my proposal.
It's not a matter of forcing the standard periodic table into a square shape. It's a true square spiral, not a set of concentric squares. If you start from the center and move counterclockwise, the elements unfold in a continuous path leading to the outermost ones.
Beyond this continuity, which is characteristic of any spiral, this layout offers additional advantages. Notably, this arrangement brings the halogen and alkali metal groups into close proximity, making it easier to connect hydrogen to both groups; and the square shape fits better onto a standard sheet of paper, and it´s easier to draw than circular shapes.
This brings me to a broader point, the practicality of representations beyond chemical considerations. A 2D model can be easily printed in textbooks, displayed on classroom walls, and viewed as a static image without the need for constructing models or (re)playing videos. While 3D models can also be accurate, they may be less convenient for everyday use.
I also took as a compliment that you found my representation easy and resembling the traditional periodic table. That similarity could make it easier for people to adopt an eventual shift from the traditional periodic table. However, arriving at this design was far from simple, and the proof is that, to my knowledge, there is no other square spiral model, despite the long-standing race to find new ways of arranging the elements.
Of course, I understand that each of us will advocate for our own representations as “the right one”. Still, I hope this message has helped clarify some aspects of mine.
Thank you for your interest and feedback,
Mario Rodríguez Peña
Jess Tauber
To view this discussion visit https://groups.google.com/d/msgid/PT-L/CAJ-%2B8fBm1xd9Kt7Qu5oa4DhEUkVZnmzbC9dag4LxbbXwVbZVEw%40mail.gmail.com.