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The INTERNET Database of Periodic Tables

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.

Use the drop menus below to search & select from the more than 1300 Period Tables in the database: 

  Text Search:       

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

1936   Orbital Filling
1936   Libedinski's Periodic Classification of The Elements
1959   Mendoza's Neuvo Sistema Periodico
1977   Ambrosis' Clasification Periodica de los Elementos
2004   Sistema Periódico Armonico de Gutierrez-Samanez
2008   Nuevo Modelo Mathemático Tabla Periódica
2010   Khipu or Quipu Periodic Table
2016   Genoma de la Materia
2018   Sistema Periódico Binodico
2018   Periodical System (Binodic Form): a new mathematical paradigm
2019   Samanez's Binodic Periodic System, New Mathematical Paradigm Poster
2021   Helix vs. Screw
2021   Rolled-up Version of Benfey's Periodic System
2022   Electronegativity Seamlessly Mapped Onto Various Formulations of The Periodic Table
2022   Vernon's Yin Yang of The Periodic Table

Year:  1936 PT id = 777

Orbital Filling With Electrons

Students of chemistry are often confused why the orbitals fill with electrons: 1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p6... etc., because the 3d10 seems to be 'out of sequence'.

This 'out of sequence' difficulity is nicely explained if the orbitals are arranged in a slightly different way:

The aufbau principle states that in the ground state of an atom or ion, electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. For example, the 1s shell is filled before the 2s subshell is occupied. In this way, the electrons of an atom or ion form the most stable electron configuration possible.

The order in which these orbitals are filled is given by the n + rule, also known as the Madelung rule (after Erwin Madelung), the Janet rule or the diagonal rule.

Orbitals with a lower n + value are filled before those with higher n + values. In this context, n represents the principal quantum number and ? the azimuthal quantum number. The values = 0, 1, 2, 3 correspond to the s, p, d and f orbital lables.

Julio Gutiérrez Samanez writes:

"I send you the diagram below that reconciles quantum mechanics (diagram for filling the electronic cells) with the Janet table or LSPT. Explaining the duplication of periods with the duplication of the quantum number n, and the introduction of Tao (T) spin of the level or spin of the period, which explains the parity of the symmetric periods."

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Year:  1936 PT id = 909

Libedinski's Periodic Classification of The Elements

Simón Libedinski: PERIODIC CLASSIFICATION OF THE ELEMENTS, from his book: Dialectical Materialism, in Nature, in Society and in Medicine, Ediciones Ercilla, Santiago de Chile, 1938, pp 56-57:

"Mendeleev's Table, like that of Werner and others, are not, however, more than flat projections of the actual ordering of the elements. There is as much difference between Mendeleev's Table and the real group as there is between the planisphere and a rotating globe. A rational representation, starting from the simplest element – the negative electron –, would be a spiral line that, surrounding said central point, first gave a small turn, touching only two bodies: hydrogen and helium. From here it would jump to a much larger orbit, in which it would touch eight bodies and then another equal, also of eight. From here, another jump to a much larger orbit, comprising eighteen bodies, and then another equal; from this point one jumps to another orbit, again augmented, comprising thirty-two bodies (including rare earths); and when this round is over, the last one begins, to vanish a short distance.

"In the dialectical grouping of the elements, which I have the satisfaction of exposing, the classic arrangement of the same is respected. Only the arrangement changes, which instead of being rectilinear, is spiral. So I managed to suppress the anomaly of the double columns, and comfortably incorporate the important group of rare earths. I can not give my graphic the name of Tabla, because it is just the opposite: it aims to give the idea of ??space, and of movement in space. The double columns of the Classic Table can be found here as well, but only if you look through the whole, considered as a planetary system of conical shape, with the electron at the vertex. Effectively: column 1 coincides, through space, with column 1a; column 4 with column 4 bis, etc. The dialectical grouping also allows us to easily appreciate the remarkable dialectical character of the properties of matter: these properties are repeated periodically. These are the "returns" to qualities or previous properties, but not exactly equal to those, but only similar: and this resemblance, only to a certain extent. The difference is that that quality, those properties or some characteristic, are exalted to each dialectical return."

Contributed by Julio Antonio Gutiérrez Samanez, Cusco, Peru, March 2018 (using Google Translation)

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Year:  1959 PT id = 1160

Mendoza's Neuvo Sistema Periodico

A memorial work, Ley De Configuraciones Electronicas, published posthumously in 1965 to honor Oswaldo Baca Mendoza (1908–1962 Cusco, Peru) and his 1959 Neuvo Sistema Periodico. Download the full PDF file (in Spanish).

Click to enlarge:

Thanks to Julio Gutierrez Samanez for the infomaton, etc.

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Year:  1977 PT id = 754

Ambrosis' Clasification Periodica de los Elementos

By Dr Raúl Julio Ambrosis, who taught Chemistry at the National University of La Plata in Argentina. The source is the Clasificación Periódica de los Elementos, Buenos Aires, Ediciones Marymar, 1977.

Click here for the full size version:

Ambrosis PT

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Year:  2004 PT id = 1100

Sistema Periódico Armonico de Gutierrez-Samanez

A digitised 2004 book by book by Julio Gutiérrez-Samanez.

Julio writes:

"These matrix tables are inspired by the method used by the Peruvian chemist Oswaldo Baca Mendoza (1908-1962).

"The tables are read in this way: The Law of Formation of nuclei generates all the horizontal series Z, is dependent on n (series of integers numbers) and a constant K = 1. In the step-to-right tables (n) it will be equal to or greater than 0. In Janet's Left-Step table, (n) will be less than or equal to (-1). The values of this series Z will serve as a constant for the second law.

"The Group Formation Law or vertical series. Its generate the numeric values of the columns either from left to right or from right to left. In system A -1: With the first law: n = 0, then Z = 1. The vertical series Zg = 1, 3 11, 19, 37, 55, 87 ... That is: 1H, 3Li, 11Na, 19K, 37Rb, 55Cs, 87Fr, 119, 169 ... Changing the values of n or Z, all the columns of the table will be obtained.

"In system A -2: With the first law: on the left, n = -1, then Z = 0. The vertical series Zg will be: 2He, 10Ne, 18Ar, 36Kr, 54Xe, 86Rn, 118Og, 168, 218. .. Similarly, changing the n or Z values, we can fills the columns of the table. In system B -1: With the first law: for n = 0, then Z = 1. The vertical series Zg will be; 1H, 3Li, 5B, 13Al, 21Sc, 39Y, 57La, 89Ac, 121, 171 ... By varying the values of n or Z, the entire table is filled. In system B -2: (Its mathematizes the Janet system). With the first law: on the left, for n = -1, then Z = 0.

"The vertical series Zg will be; 2He, 4Be, 12Mg, 20Ca, 38Sr, 56Ba, 88Ra, 120, 170, 220 ... By varying the values of n or Z, the entire table is filled. The third law of the limiting the periods or periodic law, appears graphically, by comparison between rows: For example: in table B -1, in column Z = 3, after 1H and 2He, en of the first horizontal line, the value 3 appears, which is already entered in the first column as 3Li, therefore, that part of the first horizontal row (from 3 to 50) is deleted.

"The same happens with the number 5 in column 3, which is already in the first column as 5B, therefore it will be deleted in the second row from 5 to 52. The same applies to pair 13, 21 of the column Z = 9, same, with the pair 39, 57 of the column Z = 19 and of the pair 89, 121 of the column Z = 33. For that reason the periods: P are duplicated function: 2 (1 ^ 2), 2 (1 ^ 2), 2 (2 ^ 2), 2 (2 ^ 2), 2 (3 ^ 2), 2 (3 ^ 2) .... = 2, 2, 8, 8, 18, 18, 32, 32 ... and the forms are exact and staggered. The colors represent the quantum functions: s (red), p (orange), d (yellow), f (green), g (blue)."

Read the book here (in Spanish).

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Year:  2008 PT id = 313

Nuevo Modelo Mathemático Tabla Periódica

Julio Antonio Gutiérrez Samanez presents his Periodic Table formulation ideas in a 2006 PDF paper (in Spanish):

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Year:  2010 PT id = 388

Khipu or Quipu Periodic Table

The Khipu or Quipu or Talking Knot Periodic Table, developed by Julio Antonio Gutierrez Samanez.

Google translated from the Spanish pdf file:

"As a result of bringing together each pair of periods in a single function or binod, the author has found a new regular on the subject, which has been defined as a new quantum number, since the number of orders or regulations binod growth elements in the table, under the appearance of pairs of new types of quantum structures or periods whose organization responds to a simple mathematical function: a parable of the type Y = 4 X ^ 2 - In this case report: a) That the strings correspond to pairs of periods or binod and knots are double for items with orbital s (in red), six nodes for p in orange, 10 yellow d knots and 14 knots for green f . b) That in each binod or rope, appear regularly in pairing mode or dual, new quantum or orbital structures, such as moving from within the orbital previous binod.":

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Year:  2016 PT id = 1221

Genoma de la Materia

By Julio Antonio Gutiérrez Samanez, Genome of Matter:

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Year:  2018 PT id = 936

Sistema Periódico Binodico

By Julio Antonio Gutiérrez Samanez, who writes:

"Sistema Periódico Binodico. Nuevo Paradigma Matematizado. I have followed the work of the wise Mendeleev, of Emil de Chancourtois, of Charles Janet; inspired by the work of my countryman Dr. Oswaldo Baca Mendoza. It is in Spanish but soon I will have the English version."

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Year:  2018 PT id = 946

Periodical System (Binodic Form): a new mathematical paradigm

By Julio Antonio Gutiérrez Samanez, who writes:

"System devised and prepared by the Peruvian chemical engineer, Julio Antonio Gutiérrez Samanez, deals with a new conception of Mendeleev's Law as a mathematical function and a new description of the process of forming the series of chemical elements according to mathematical laws and dialectical processes of changes quantitative and qualitative under a dynamic spiral architecture in 3D, which is postulated as a new scientific paradigm."

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Year:  2019 PT id = 1064

Samanez's Binodic Periodic System, New Mathematical Paradigm Poster

Julio Antonio Gutierrez Samanez (Master's student in chemical engineering at the San Antonio Abad National University of Cusco, Peru) presented a poster at the 4th International Conference on the Periodic Table arranged by IUPAC, Saint Petersburg, Russian Federation, July 2019. See the high resolution .PDF file.

More here and at        

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Year:  2021 PT id = 1186

Helix vs. Screw

Julio Antonio Gutierrez Samanez writes:

Until today, when they write about the work of Chancourtois and his telluric helix wound in a cylinder, still no one alludes to this other telluric helix wound in a cone or screw, the idea is the same: a rope that winds a geometric solid.

The first was devised in 1862, the other in 2008 (146 years later). But, there is a big epistemological difference. In the first, the elementary series presented was: 8, 8, 8, 8, 8 ..., etc., in the second it is: 2, 2, 8, 8, 18, 18, 32, 32. Furthermore, the division of conical radii is regulated by the function 2 (n ^ 2) = 2, 8, 18, 32...

Each binode has two spirals or two periods with the same number of elements, which correspond to the function 4 (n ^ 2). I don't think it is a discovery, it is just the conclusion of the contributions of Rydberg, Janet, and, of course, Chancourtois.

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Year:  2021 PT id = 1222

Rolled-up Version of Benfey's Periodic System

Rolled-up Version of Benfey's Periodic System by Julio Antonio Gutiérrez Samanez. More on the YouTube video here.

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Year:  2022 PT id = 1241

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:

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Year:  2022 PT id = 1252

Vernon's Yin Yang of The Periodic Table

René Vernon writes:

"I was prompted to [develop] this item after reading Eric Scerri's open access article: In Praise of Triads. The nub of Eric’s article is to argue for the LST on the grounds of triad regularity, first-row-anomaly regularity, and consistency with QM.

"It occurs to me that efforts to introduce more regularity to the PT invariably introduce new irregularities elsewhere. For example, as far as triad regularity goes, the left step table (LST) with He over Be introduces its own anomaly in that no element in period 1 (H, He) is part of a triad whereas this is not the case for all periods thereafter. In contrast, all periods of the traditional table have at least one element that is part of a triad.

"As far as QM goes, this tells us that there is a theoretical regularity to the PT. This regularity can be used to inform e.g. the LST, ADOMAH or Julio’s binodes. But such depictions do not reflect the factual relationships we see amongst the chemistry of the elements as well as is the case for the conventional form. A most obvious example is that the LST, while being more consistent with QM, disrupts the bottom-left to top-right trend in metallic to nonmetallic character seen in conventional tables.

(I must caveat that I'm referring to the chemistry of the elements in conditions regularly occurring on Earth. For example, it has been reported that under sufficiently high pressures the elements change their EN and electron configurations. If so, this suggests a need for a different table at high pressure.)

At this point, the chemistry educators enter the picture. They move the s-block to left. Helium is relocated over Ne on the basis of its nobility. (This could change if a few compounds of He were to be synthesized). Somewhat similarly, La was discovered well before Lu, so it ended up under Y, and most folks see no good reason to replace La with Lu. Sure, in the 32-column form, the result is a split d-block but the infrequency with which the 32-column form appears is such that most people are not bothered. The result is the conventional table.

Philosophically, while the n+l based LST might represent the most general form of table, the conventional table appears to currently represent the most pragmatic derivation for chemists and chemistry educators.

Since the PT is classification rather than theory, and there will thus always be hard cases at the boundaries, there will invariably be minor variations in the depiction of the conventional table with respect to e.g. the placement of H, the composition of group 3, or the length of the f block.

And there will always be tables such as MR that focus on particular perspectives of relationships among the the elements.

I’ve tried to sketch what's going in the attached image:"

Click to enlarge.

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What is the Periodic Table Showing? Periodicity

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