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There are thousands of periodic tables in web space, but this is the only comprehensive database of periodic tables & periodic system formulations. If you know of an interesting periodic table that is missing, please contact the database curator: Mark R. Leach Ph.D.

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Periodic Tables referencing the text string "Tsimmerman", listed by date:

Corbino's Right-Step Periodic Table

Published in the same year as Janet's Left-Step formulation, Corbino OM (1928) Riv Nuovo Cimento 5:LXI (and from here) produced a Right-Step version.

Commenting on this formulation, Valery Tsimmerman writes:

"Corbino saw what Janet failed to see: If blocks shifted by corresponding value of quantum number l, then the rows represent electronic shells and Janet saw what Corbino fained to see, namely the Janet rule, also known as Madelung rule. Both used rectangular boxes, but neither noticed the perimeter rule."

Thanks to Valery T for the tip!

100 Years of the Periodic Law of Chemical Elements

A Soviet Union publication in Russian celebrating Medeleeve's seminal work of 1869: 100 Years of the Periodic Law of Chemical Elements, X Centennial (Jubilee) Mendeleev Congress. The work is the product of 23 Authors. (Thanks to Ann E. Robinson, René Vernon & Valery Tsimmerman for the info.)

Fet's Periodic Tables

Two periodic tables by A.I. Fet from his book, "Mathematical Modeling in Biology and Chemistry. New Approach" Nauka, Sib.Dep., 1992.

Larry Tsimmerman writes:

"First formulation, Tab. 7, is precursor of Adomah PT with broken Z-sequence and questionable pairing of elements in accordance with "ml". Tab. 8 is a Janet LST shown vertically. Fet discusses Periodic Table in the light of Group Theory. (The book was sent to me by Eric Scerri and it was signed by Fet for Hefferlin)."

ADOMAH Periodic Table by Valery Tsimmerman

The ADOMAH periodic table is based on the Janet or left-step periodic table. It consists of four blocks (s, p, d & f) corresponding to quantum numbers l = 0,1,2,3. Blocks are separated, shifted and reconnected with each other via diagonal lines. This arrangement creates "layers" or "strata" that retain continuity in respect to atomic number Z, in addition to usual columns and rows. Therefore, numbers shown on the right hand side of the table may represent either quantum numbers n (electronic shells) if horizontal rows are followed, or n + l if "layers" or "strata" are followed.

This feature assists in creation of electronic configurations of the elements. Elements H and He are placed in two positions that reflect their dual nature and give proper consideration to atomic structure and chemical properties of those two elements. This feature also preserves triads He, Ne, Ar and H, F, Cl. Also, the elements are placed in rectangular "boxes", so any two of such "boxes" make up a square thus symbolising electron pairs. This also cuts table length in half. Unlike the Janet table, this table is assembled from bottom up in direction of increase of quantum number n, as well as atomic weight and energy. The ADOMAH table has symmetry and, assuming total number of elements 120, can be divided in four parts of 30 elements with center point located among precious metals.

Extending the Periodic Table

The periodic table now extends to element 118, Oganesson, and scientists are attempting to go further. Below is part of a Segre chart, proton number on the y-axis and neutron number of the x-axis, from a report from the Japanese Superheavy Element Laboratory, RIKEN Nishina Center, RIKEN.

The diagram shows various nuclear reactions, for example: ²³²Th + ⁴⁰Ar to make ²⁷²Hs.

Thanks to Larry Tsimmerman for the tip!

ADOMAH Tetrahedron

Valery Tsimmerman has developed various periodic table formulations, available at perfect perioidic table.com.

Nucleosynthesis Periodic Tables

The buildup of heavy elements from lighter ones by nuclear fusion.

Helium, and some lithium, was produced by cosmic (or primordial) nucleosynthesis from 2 to 20 minitues after the Big Bang, here and here:

From the Encyclopedia of Science:

Today most element-building nucleosynthesis takes place in stars.

Stellar nucleosynthesis converts hydrogen into helium, either by the proton-proton chain or by the carbon-nitrogen-oxygen cycle. As a star evolves, a contracting superdense core of helium is produced from the conversion of hydrogen nuclei into helium nuclei.

Eventually, the temperature and pressure inside the core become high enough for helium to begin fusing into carbon. If the star has more than about twice the Sun's mass, a sequence of nuclear reactions then produces heavier elements such as oxygen, silicon, magnesium, potassium, and iron. Successively heavier elements, as far as iron (in the most massive stars) are built up in later stages of stellar evolution by the triple-alpha process. The heaviest elements of all are produced by explosive nucleosynthesis in supernova explosions, by mechanisms such as the p-process, r-process, and s-process:

From FigShare (Athanasios Psaltis):

Our quest to explain the origin of the elements started in the late 1950's by two famous papers independently - E. M. Burbidge et al., Rev. Mod. Phys. 29, 547 (1957) & A.G.W. Cameron, Pub. Astron. Soc. Pac. 69, 201 (1957) - whose authors claimed that the elements are created in astrophysical environments. This is the well-known periodic table of elements, but where each element is labeled by the environment that is created (e.g Supernova explosion etc.).

In 2017 the LIGO gravitional wave detector identified the merger of two neutron stars, an event which produces large quantities of gold, platinum etc. Thus, an updated periodic table of nucleosyntheis looks like this, from an interesting SDSS blog:

Conal Boyce has prepared a Janet Left-Step Nucleosynthesis Periodic Table. Conal writes:

"This formulation was created by mapping the Ivans/Johnson color-coding scheme onto a Janet grid, using Tsimmerman half-cells. Although several attempts to contact Professor Jennifer Johnson failed, I did receive enthusiastic feedback on this LST mapping from Professor Inese Ivans, and decided to make it public on that basis."

Click to enlarge:

Mathematical Expression of Mendeleev's Periodic Law

Valery Tsimmerman, of the ADOMAH Tetrahedron periodic table formulation and the Perfect Periodic Table website, presents a Mathematical Expression of Mendeleev's Periodic Law:

3D Left Step Periodic Table

By Masahiko Suenaga, Kyushu University, Japan a 3D Left Step Periodic Table.

"Inspired by the work of Dr. Tsimmerman and Dr. Samanez, I have created a new 3D Left Step Periodic Table, which resembles to Mt. Fuji, recently registered as a World Heritage site. For more information, please visit my website":

ADOMAH Periodic Table Glass Cube

Valery Tsimmerman, of the ADOMAH Periodic Table and the ADOMAH Tetrahedron, has now used these ideas to produce a beautiful glass cube:

This amazing object is available for sale from Grand Illusions:

A Note by Philip Stewart stewart.phi@gmail.com

The cube represents 120 chemical elements etched into a cube of Optical Crystal glass. The s, p, d, and f blocks of the Janet periodic table form four rectangles, which are slices of a regular tetrahedron, parallel with two of its edges and with two faces of the circumscribed cube. All four quantum numbers are made visible in this arrangement. You can see a 2-D version on the Perfect Periodic Table website, click on the "skyscraper" version on the right to see the tetrahedron, and go to Regular Tetrahedron at foot of page for details.

The regular tetrahedron is the only form in which slices are rectangles of different shape and identical perimeter. When each orbital is represented by a square of unit edge, the rectangles representing the blocks all have the same perimeter, which is twice the length of the edges of the tetrahedron (which are of course √2 times the edges of the cube): 18 units = 2(values of n + values of m_l).

Valery Tsimmerman, orahct@gmail.com, creator of the design, has written to me as follows:

"I just had some thoughts about the Perimeter Rule that is at the basis of the tetrahedral arrangement. Dimensions of the blocks are dictated by number of values of ml and number of values of n. We know that n governs quantization of energy. Recently I learned that quantization of the possible orientations of L with respect to an external magnetic field is often referred to as space quantization. (Serway, Jewett: Physics for Scientists and Engineers. 6th edition. p.1369).

"That is, m_l stands for space quantization. Therefore, the Perimeter Rule reflects a direct relationship between energy and space. I think that this could have some significance. The beautiful thing about the Universe is that each type of symmetry is related to some conservation law. Symmetry in time is related to energy. Therefore, n is related to time also, so, in the Perimeter Rule we have relationship between time and space on quantum numerical level. The interesting thing is that m_l can be positive and negative, while n can only be positive. Similarly, things can move in space in positive and negative directions, but time has only one direction. There is no negative time, just as there are no negative values of quantum number n."

Adomah is a variant of Adamah, Hebrew for 'dust of the earth', from which Adam was made (Genesis 2:7).

Janet Rajeuni

By Philip Stewart:

Janet Rejuvenated, with acknowledgement to Mazurs and to Valery Tsimmerman for the idea of using one square per orbital and of shifting the blocks so that each row represents one value of n, the principal quantum number.

The main objection people make to Janet is that He is placed at the head of the alkaline earth metals although it behaves as a noble gas. The essential answer is that electronic structure explains behaviour and not vice versa; like Ne (and unlike Ar, Kr, Xe and Rn), He has a complete shell. Similarly H, like C, is half way between a full and an empty shell, unlike the alkali metals and the halogens. I suggest a new argument: nobody finds it strange that the p block has a row of non-metals at its head (and that half its members are non-metals), so why not the s block?

ADOMAH Periodic Table and Normal Distribution

Valery Tsimmerman writes:

The ADOMAH, from here, resembles the normal distribution or "Bell Curve". It also mimics the distribution of electrons in orbitals:

New Rendering of ADOMAH Periodic Table

From Valery Tsimmerman, of the PerfectPeriodicTable.com and the ADOMAH Periodic Table:

"I received email from Dr. Marcus Wolf who is a chemist, working on renewable energy and electrochemical storage in Germany, near Nuremberg. He also lectures at Georg Simon Ohm, Technische Hochschule Nürnberg. Attached to his email was new version of ADOMAH Periodic Table that he created. In this new rendering he is using Jensen's Valence Manifold (VM)."

This is what Dr. Marcus Wolf wrote:

"The first one to come up with the idea of using a valence manifold VM = [e + v] as a label for the groups, was Will B. Jensen. He derived it from the very early attempts of Richard Abegg, who, at around 1904, brought up the hypothesis of 'main- and counter-valences', derived from the observable behavior of elements and their compounds in electrochemical experiments. Eric Scerri is citing Jensen in his latest book, in the chapter about Richard Abegg. But Jensen's proper article from 1983 or so is far more detailed and in his later publications he then introduces the valence manifold concept. Last weekend I accidentally observed another consistency between the G-values and their ordering and the valence electron counts, e. If you fix the e value of the starting group in a given l-block as e(initial), you could generate every G-number of a given group by adding the valence vacancy count, v, to it:

G = e(initial) + v.

"That is another hint for the consistency of the VM labelling concept."

Stewart's Chemosphere

P J Stewart, a good friend of the periodic table database, has mapped a PT onto a sphere.

PJS writes: "It is Janet Rajeuni 2014  wrapped round a sphere, going back to Mazurs 1965, and Tsimmerman 2006.  Arabic numerals indicate shells (values of principal quantum number); Roman numerals indicate periods."

Telluric Remix

Philip Stewart writes:

The Telluric Helix (La Vis Tellurique) was the first graphic representation of the periodic system of the elements, conceived as a spiral wound round a cylinder. It was designed in 1862 by Alexandre-Émile Béguyer de Chancourtois, a French mineralogist. 'Telluric' is from Latin tellus, earth, recalling the 'earths', oxides, in which many elements had been discovered.

My 'Telluric Remix' is a return to the cylinder. It combines ideas from Charles Janet (8, not 7, periods, ending with ns2, defined by a constant sum of the first two quantum numbers, n and l), Edward Mazurs (all members of each electron shell in the same row) and Valery Tsimmerman, (a half square per element).

• The Telluric Remix is topologically the same as my 'Janet Rajeuni' and 'Chemosphere': it maintains the continuous sequence of atomic numbers with the help of arrows, which cascade down, displaying graphically the Janet [Madelung] rule for the order of subshell filling.
• I have placed the s block in the centre to emphasise its pivotal nature and so that there is no question of whether it belongs on the left or on the right. Every shell (Arabic numeral) and every period (Roman numeral) ends with ns², but the ns electrons combine with f, d or p electrons of elements in the succeeding period to make their valence shells, until ns²+np⁶, which forms a noble gas. Helium, He, is also noble with a complete n=1 shell and no 1p⁶.
• Noble gases are marked G. Groups are numbered sequentially within each block, and in general the xth member of the series has x electrons in the subshell. Exceptions are shown by a small d (or two) in the corner, signifying that a d electron replaces an s electron in the d block or an f electron in the f block (note also p in Lr). This makes it easy to determine the electronic structure of each element.
• Click here for a larger version.

The printable version is available (click here for the full size version) to make your own:

I have not claimed copyright; please copy and share but acknowledge my authorship. stewart.phi@gmail.com

Janet's Left-Step with Ground Level Microstates

By Valery Tsimmerman, who writes:

Janet's LST with ground level microstate information and total spin graph shown for each group of elements. The top line represents number of electrons in open sub-shells (with exception of six anomalous elements). Information shows physical (spectroscopic) basis of the groups.

The zigzag line on top is a graphic representation of Hund's rule showing the total inherent spins of atoms and the total spin of Cu is 1/2, same as for Ag and Au. When it comes to ground level atomic microstates and Hund's rule Cu is not anomalous (2S1/2), despite its anomalous electron configuration.

The diagram represents Hund's Rule that states that "the lowest energy atomic state is the one that maximizes the total spin quantum number for the electrons in the open subshell" (Wikipedia). Y-axis is the total spin and x-axis is number of electrons in open shells (with exception of six anomalous elements).

First, I would like to make couple of general comments. When discussing periodicity, they typically talk about chemical properties and electron configurations/differentiating electrons, etc, but those are not specific enough. For each electron configuration there are multiple microstates. For example, for single electron configuration of carbon there are over 30 microstates and only one of them corresponds to ground level. So, microstates express combined physical/spectroscopic properties of whole atoms and, the most important, combined properties of electrons located in open subshells.

Now, look at ground level term symbols in each group. I see amazing consistency, especially in the main groups. It tells me that groups are not only chemical, but physical!

Looking at periods one can see that all periods in s, p & d blocks begin with elements that have multiplicity M=2 and end with M=1. This is also true for f-block if it starts with La and Ac and ends with Yb and No. This puts Lu and Lr firmly in group 3. Placing La and Ac in group three ruins spectroscopic consistency.

Click here image to enlarge the PT below.

ADOMAH Periodic Table Formulation with NIST Data

By Valery Tsimmerman, who writes:

I would like to share with you another variant of my ADOMAH periodic table formulation that holds additional spectroscopic information.

Click here image to enlarge the PT below.

Simpson's 4-Dimensional Version of the ADOMAH Periodic Table

Doug Simpson writes:

"Valery Tsimmerman's ADOMAH table and website got me started as a periodic table hobbyist. The attached photos show what I've been up to. Valery's observation that n, l, & m conspire to generate a half-filled tetrahedral lattice inspired me to create a 4D periodic table using all four quantum numbers as coordinates."

Janet Rejuvenated: Stewart-Tsimmerman-Nawa

An updated version of Philip Stewart's Janet Rejuvenated by Valery Tsimmerman redrawn by Nawa.

Click here to enlarge.

Telluric Remix in Colour

Philip Stewart writes (this is the same text that accompanies the 2018 B/W version):

The Telluric Helix (La Vis Tellurique) was the first graphic representation of the periodic system of the elements, conceived as a spiral wound round a cylinder. It was designed in 1862 by Alexandre-Émile Béguyer de Chancourtois, a French mineralogist. 'Telluric' is from Latin tellus, earth, recalling the 'earths', oxides, in which many elements had been discovered.

My 'Telluric Remix' is a return to the cylinder. It combines ideas from Charles Janet (8, not 7, periods, ending with ns2, defined by a constant sum of the first two quantum numbers, n and l), Edward Mazurs (all members of each electron shell in the same row) and Valery Tsimmerman, (a half square per element).

• The Telluric Remix is topologically the same as my 'Janet Rajeuni' and 'Chemosphere': it maintains the continuous sequence of atomic numbers with the help of arrows, which cascade down, displaying graphically the Janet [Madelung] rule for the order of subshell filling.
• I have placed the s block in the centre to emphasise its pivotal nature and so that there is no question of whether it belongs on the left or on the right. Every shell (Arabic numeral) and every period (Roman numeral) ends with ns², but the ns electrons combine with f, d or p electrons of elements in the succeeding period to make their valence shells, until ns²+np⁶, which forms a noble gas. Helium, He, is also noble with a complete n=1 shell and no 1p⁶.
• Noble gases are marked G. Groups are numbered sequentially within each block, and in general the xth member of the series has x electrons in the subshell. Exceptions are shown by a small d (or two) in the corner, signifying that a d electron replaces an s electron in the d block or an f electron in the f block (note also p in Lr). This makes it easy to determine the electronic structure of each element.
• Click here for a larger version (pdf).

I have not claimed copyright; please copy and share but acknowledge my authorship. stewart.phi@gmail.com

Kultovoy's Periodic Table Book

Nicolay Kultovoy, website, as sent me a copy of his Periodic Table book, entitled [Google Translate]: Book 5. Part 11-08. A single quantum mechanical model of the structure of the atomic nucleus and the periodic table of chemical elements of D.I. Mendeleev.

In a mixture of Russian & English, the PDF of the book can be viewed here.

Chapter 1. Triune (electrons, nucleons, chemical elements) quantum mechanical model of Colt. Three
1.1 the Rules of filling of the orbits of electrons.
1.2 Pyramidal lattice.
1.3 models with cubic sieve.
1.4 models with face-centered lattice.
1.5 quantum Mechanical form of the periodic table of chemical elements.
1.6 Stowe-Janet-Scerri Periodic Table.
 
Chapter 2. A lattice model of the nucleus. Model 62
2.1 Berezovsky G. N.
2.2 I. Boldov
2.4 Konovalov.
2.5 Manturov V.
2.6 Semikov S. A.
2.7 alpha-partial model of the atomic nucleus.
2.8 Burtaev V.
 
Chapter 3. Various lattice (crystal) model of the nucleus of an atom. One hundred five
3.0 Luis Pauling.
3.1 Valery Tsimmerman. ADOMAH Periodic Table. Model 3-2.
3.2 Klishev B. V. Model 3-1.
3.3 Garai J. Model 3-1.
3.4 Winger E Model 4-2.
3.5 Norman D. Cook. Model 4-1.
3.6 Gamal A. Nasser. Model 4-1.
3.7 D. Asanbaeva Model 4-1.
3.8 Datsuk V. K.
3.9 Bolotov B.
3.10 Djibladze M. I.
3.11 Dyukin S. V.
3.12 A. N. Mishin.
3.13 M. M. Protodyakonov
3.14 Dry I. N.
3.15 Ulf-G. Meißner.
3.16 Foreign works.
 
Chapter 4. Long-period periodic table. One hundred eighty one
4.1 long-Period representation of the periodic table.
4.2 Artamonov, G. N.
4.3 Galiulin R. V.
4.4 E. K. Spirin
4.5. Khoroshavin L.
4.6 Step form proposed by Thomsen and Bohr.
4.7 Symmetrical shape of the periodic table.
 
Chapter 5. Construction of a periodic table based on the structure of orbitals. Two hundred twenty one
5.1 construction of the periodic table on the basis of orbitals.
5.2 Short V. M.
5.3 Kulakov, the Novosibirsk table of multiplets.
 
Chapter 6. Atomic structure. Two hundred forty eight
6.1 Table of isotopes.
6.2 the structure of the orbitals.

Stewart's Quantahedron Formulation

From Philip Stewart, here & here, comes a three dimensional Quantahedron Formulation.

Philip writes:

"The Quantahedron is based on Tsimmerman's Adomah cube, realised in transparent plastic, in the usual order in which Z values are read, printed on separable blocks so that it can be assembled."

Rainbow Periodic Table in ADOMAH Cube

From the prolific Nagayasu Nawa, a version of his Rainbow Periodic Table inside Valery Tsimmerman's glass cube:

Electronegativity Seamlessly Mapped Onto Various Formulations of The Periodic Table

A discussion on the Google Groups Periodic Table Discussion List, involving a René Vernon, Nawa Nagayasu & Julio Samanez (all contributors this database) lead to the development of the representations below, showing electronegativity seamlessly mapped onto a modified Left-Step Periodic Table:

Nawa Nagayasu has mapped electronegativity to Mendeleeve's formulation:

Nawa Nagayasu has mapped electronegativity onto other formulations, Julio's Binode Spiral:

Courtine's 1926 formulation:

and the "conventional", short, medium and long forms of the periodic table with hydrogen above and between B & C which show the botom-right-to-top-left electronegativity trend:

Jeff Moran's Spiral:

René Vernon's 777 Periodic Wedding Cake:

Valery Tsimmerman's ADOMAH formulation:

Valery Tsimmerman's ADOMAH tetrahedron (in a glass cube) formulation:

© Mark R. Leach Ph.D. 1999 –

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