Janet LSPT Program
- This tool generates a Janet Left-Step Periodic Table (JLSPT) through an algorithm and without using chemical information. This type of tables do not organize elements according to the ordering and numbering system recommended by IUPAC. Therefore, the generated rows and columns not necessarily correspond to the periods and groups found in chemistry textbooks. Users can generate specific atomic number sequences (Z values) by specifying row and column ranges.
To use the tool, proceed as follows.
- Complete and submit form.
- To explore super heavy elements, up to Z = 220, set the number of rows to be displayed from 1 to 10 and columns from 1 to 50.
- To retrieve Z values only, check the Z only checkbox before submitting the form.
- To remove any display distortions, resize the output by pressing down the keyboard
Ctrlkey while pressing the "-" or "+" keys as many times as necessary.
- Periodic tables are mental constructs that emphasize chemical or physical properties according to the preferences of their proponents. In these constructs, rows are called periods and columns groups. Periodic tables are mere abstractions of the Periodic System of Elements (PSE).
So far, IUPAC has no official form of the PSE, and an IUPAC-approved form of a periodic table does not exist. The only specific recommendation IUPAC has made concerning the periodic table covers the Group numbering of 1-18 (Leigh, 2009). Some prominent members of IUPAC accept that this convention is not ideal for every purpose, that teachers might find that it does not fulfill all their requirements, and that it is not strictly consistent with some notions of electronic structure. But then they stick to tradition, making their case more an appeal to authority issue or a tribute to old glory days than anything else.
Over the years, all kind of periodic tables have been published: 18-group labeled, 32-group labeled, unlabeled, rectangulars, triangulars, tetrahedrals, cubic, rounded, stacked, spiral-like, galaxy-like, and even fractal-like (Bradley, 2011; Stewart, 2007). Some of these so-called "tables" are not even tabular arrangements. At the time of writing, there is no consensus on which periodic table is the "correct", "best", or "optimal" one, and IUPAC requisites do not really help.
- About this tool
This tool was developed, not to validate any particular version of the periodic table or to produce one that accounts for electron configuration anomalies, but to investigate whether those that have been proposed, "optimal" or not, can be modeled with algorithms; i.e., if a periodic table arrangement can be stored as a computer algorithm and called when needed.
By doing so, by no means our goal is to reduce chemical periodicity to math operations, but to identify when this can be done. If a model is found, it could be used to generate, store, retrieve, and mine atomic sequences, build new tools based on those sequences, and make predictions about the existence of yet-undiscovered elements.
- Modeling Periodicity
Although modeling chemical periodicity is not easy, it is not an impossible or illusory task. Actually this has been done in the past, but as exercises for finding triads (Scerri, 2008) and atomic number series rather than for modeling entire periodic tables or the PSE.
In the quest for finding mathematical frameworks for modeling atomic number sequences, we have identified a few interesting ones. One is described by Tsimmerman (2012); the others by Garai (Judge, 2009a, 2009b; Garai, 2003, 2008a, 2008b, 2010, 2011a, 2011b, 2015), and Perez (1997, 2015a, 2015b, 2015c). These authors kindly sent us copy of their work. Our current tool is based onTsimmerman's. Research work along other frameworks is currently under way.
- Tsimmerman's Framework
Tsimmerman (2012) has described a mathematical expression of Mendeleev's Periodic Law that generates atomic number (Z) sequences. This approach consists in first computing atomic numbers (A) of alkaline earth metals from period numbers (p) and then adding group numbers (g), like this:
Z = A + g
A = (1/6)[(p+1)3 + (1/2)(p+1) + (3/2)(p+1)(-1)p-1]
where g is a value with boundaries
(1 - L) ≤ g ≤ 0
L = (1/8)[2p + 1 + (-1)p-1]2
p = 1,2,3...
and where L is the length of a period.
The convention adopted here is to define g as a negative value, in order for the periodic table to be left step.
- Framework Evaluation
We have written a computer program that evaluates the above expressions by looping over "p" (p = 1, 2, ...) and "g" (g = 0, -1, g = -2, ...) values. Figure 1 shows its raw output.
Figure 1. Program raw output.
When we organized the output shown in Figure 1 in a tabular form and shifted all cells to the right, the result was a Janet Left-Step Periodic Table (Wikipedia, 2015a; 2015b; Siegfried, 2015; Stewart, 2009). See Figure 2.
Figure 2. Program output resembling Janet table.
Consequently, we can transmit a left-step representation of the Periodic System of Elements, not by sending a file, but by executing a few lines of codes. The program can then be used as a base framework for building chemistry tools on top of it.
Output Labeling Conventions
We color-coded table cells and did not show element symbols to grab the readers attention to the spdf-blocks. Why? Please keep reading.
After running the program, you may realize that the program labels columns from right to left, starting not at g = 0, g = -1, g = -2..., but at g = 1, g = 2, g = 3, and so forth. Essentially the program rescales the indices by applying the affine transformation g = a*g + b, where a = -1 and b = 1; i.e., by multiplying g label values by -1 and adding 1. No reordering was involved.
Said rescaling avoids any reference to a "group" 0 of elements and "negative groups" of elements. This is a cosmetic change.
It is true that to conform to IUPAC numbering convention of groups we could have relabelled the first two columns at the right to read g = 2 and then g = 1. We did not do that for two reasons:
- The output of our program is what it is. It orders chemical elements according to Tsimmerman's framework; no more, no less.
- We believe that simply relabeling the first two right columns is a subjective exercise based on a chemistry pre-knowledge and one that defeats the gist of our research: The testing of mathematical models that attempt to make predictions.
On the other hand, we want to acknowledge IUPAC accepted labels, so we finally settled for a happy medium and included them after a forward slash. These are the red labels that you see at the top-right corner of the table.
However, we stick to the thesis that whether IUPAC or chemists reorder or label periods and groups of the PSE according to their preferences or chemistry preknowledge is a subjective exercise after the facts.
Some proponents of Janet's LSPT adopt an IUPAC-like numbering system, but then hold back and do no label columns after the 18 mark, failing to be consistent with their own mental construct of equating columns to groups.
To address these notation issues, and other usability issues, we have implemented several modifications to the program. These are detailed below.
As of January 1 of 2016, we added the following alternative system which consists in labeling groups based on the filling of outermost subshells according to Madelung Rule; i.e., by assuming that atoms are free neutral particles in vacuum (Wikipedia, 2015b).
We can expand this system in a straightforward manner to label groups of superheavy and not yet discovered elements, up to Z = 220 (Pershina, 2009; Saito, 2000; Umemoto and Saito, 1996).
The notation used is more descriptive and convey more information. For instance, any reference to the "s1 group" means exactly this:
"The group of chemical elements with one electron in their outermost s subshell."
Many teachers and chemists will find that labeling groups in this way is more consistent with their notions of electronic structure.
A form-based user interface was initially added so users can retrieve specific Z sequences of known and not-yet discovered elements.
As it is now, the program output can be used to easily generate Janet periodic tables and other types of periodic tables. For instance, we can map atomic numbers to chemical symbols and label columns using IUPAC 18-group numbering convention, if we wish to do so. In this way we can reproduce one of the Janet periodic table versions referenced by Leigh (Leigh, 2009). We can also use the program to develop interactive tools on top of it and that accept atomic numbers as their input.
Janet Left-Step Periodic table organizes elements according to orbital (subshell) filling. The order in which these are filled is given by the n + l rule, also known as the Madelung, Janet, or Klechkowski Rule. Adomah PT is also essentially the Madelung Rule, and even more so than Janet's LSPT.
However, as indicated in a recent tutorial, the Madelung Rule assumes a non-realistic scenario wherein atoms are considered free neutral particles in vacuum with no interactions with other atoms or themselves. Obviously, the electron configuration of a chemically bonded atom can be different from the one predicted by the Madelung Rule. To Madelung's credit, his rule is only good for groups 1 and 2 (i.e., s- and p-block elements).
Diagrams describing Madelung Rule have been used as mnemonics for writing electron configurations, can be found elsewhere, and look like this
Figure 3. Electron filling diagram.
So it is not surprising that rotating by 180 degrees Figure 2 produces a shape that, statistically speaking, resembles those diagrams:
Figure 4. Inverted Janet-like table, with content removed to highlight its similarity with Figure 3.
Of the many two-dimensional mental constructs that have been proposed to describe chemical periodicity, this one resembles, at a large scale level, the subshell filling pattern observed at atomic scale levels, with element anomalies ignored (Scerri, 2012a; 2012b; 2013). The notion of statistically similar patterns emerging at different length scales of observations is the signature of fractal geometry.
Figure 4 can be used to help students understand the connection between electron orbital filling and Janet LSPT. For those that still want to follow IUPAC, they can use their 18-group numbering system. They can also use a shorter version by placing lanthanoides and actinoides as separate sections resembling footers or headers, at the expense of diluting the above self-similarity argument, like this
Figure 5. Inverted Janet-like tables with sections resembling footers and headers.
If these flipped versions are not visually appealing to teachers or students, or do not satisfy their needs, another alternative is to keep the original orientation and flip instead Figure 3, the electron filling diagram.
Last, but not least, we want to emphasize that Madelung Rule is an idealized limiting rule; hence, it cannot be applied arbitrarily to all atoms of the periodic table, and certainly, in most cases, not to chemically bonded atoms—for that you need to use the Rydberg Rule which also maximizes (n + l) values.
To write empirically correct electron configurations, we now recommend Madelung Rule for groups 1 and 2, and Rydberg Rule for groups 3 to 18 (according to the IUPAC numbering system). The tutorial A novel mnemonic for the Rydberg Rule explains the conceptual differences between these two rules and provides useful mnemonics for properly writing electron configurations.
We would like to thank Tsimmerman, Garai, and Perez for providing valuable comments and references of their work.
- 07-09-2018: Elements 113, 115, 117, and 118 were renamed according to IUPAC's 2016 naming convention (IUPAC, 2016).
- 01-21-2017: Content was edited.
- 03-09-2016: Content was edited.
- 02-10-2016: Checkbox state modified and renamed. Link to tutorial added and sections content reworked.
- 01-07-2016: References on superheavy elements (Z > 120) added.
- 01-01-2016: Alternative s,p,d, and f labels notation added.
- 12-30-2015: New content to Instruction and What is Computed? sections added.
- 12-06-2015: Transliteration of atomic numbers greater than 120 added.
- 12-05-2015: Show/hide symbols checkbox added.
- 12-04-2015: Acknowledgement section was added.
- 12-03-2015: Reference section was modified to include new citations.
- 12-02-2015: User interface was modified to allow for the automatic retrieval of triads. For instance, submitting the 6-8 periods and 1-18 groups retrieves an entire block of atomic number based triads.
- Bradley, D. (2011). Periodic Debate. ChemistryViews. June, 2011. Wiley-VCH Verlag.
- Garai, J. (2003). The double tetrahedron structure of the nucleous. Arxiv.org. 15, 9, 2003.
- Garai, J. (2008a). Mathematical formulas describing the sequences of the periodic table. J Quantum Chem 108: 667-670, 2008.
- Garai, J. (2008b). Analytical Solution Describing the Periodicity of the Elements in the Periodic System .
- Garai, J. (2010). Upper bound on the disordered density of sphere packing and the Kepler Conjecture.
- Garai, J. (2011a). Nuclear lattice model and the electronic configuration of the chemical elements.
- Garai, J. (2011b). Digital Description of the Periodic System.
- Garai, J. (2015). Debreceni Egyetem Unideb - Faculty Contact Page.
- Garcia, E. (2015). Program for reproducing Janet LSPT.
- IUPAC.org (2016). IUPAC is naming the four new elements nihonium, moscovium, tennessine, and oganesson.
- Judge, A. (2009a). Periodic Table: predictive formulations.
- Judge, A. (2009b). Periodic Table: predictive formulations.
- Leigh, G. J. (2009). Periodic tables and IUPAC. Chemistry International. 31, 1, 2009.
- Perez, J. C. (1997). 1997 : The discovery by jean claude perez of the Mendeleiev's periodic table predictive formula.
- Perez, J. C. (2015a). Jean-Claude Perez - Wiki.
- Perez, J. C. (2015b). Jean-Claude Perez - Blog.
- Perez, J. C. (2015c). Jean Claude-Perez - Google Plus.
- Pershina, V. (2009). Electronic structure and chemical properties of superheavy elements. Russian Chemical Reviews 78 (12) 1153-1171.
- Saito, S. (2000). Electronic Structure of Superheavy Elements JAERI-CONF--2000-002.
- Scerri, E. (2008). The Role of Triads in the Evolution of the Periodic Table: Past and Present. J. Chem. Educ., 2008, 85 (4), p 585 DOI: 10.1021/ed085p585. PDF version.
- Scerri, E. (2012a). Trouble in the periodic table. Education in Chemistry. January, 2012.
- Scerri, E. (2012b). The Periodic Table: A Very Short Introduction. Paperback; Oxford University Press.
- Scerri, E. (2013). The trouble with the aufbau principle. Education in Chemistry. November, 2013
- Siegfried, T. (2015). Old periodic table could resolve today's element placement dispute. Science News. April, 2015.
- Stewart, P. J. (2007). A Century on from Dmitrii Mendeleev: Tables and Spirals, noble gases and Nobel Prizes. Foundations of Chemistry. 9, 235-245.
- Stewart, P. J. (2009). Charles Janet: unrecognized genius of the periodic system. Springer Science+Media B.V. 2009. DOI 10.1007/s10698-008-9062-5
- Tsimmerman, V. (2012). Mathematical Expression of Mendeleev's Periodic Law.
- Umemoto, K. and Saito, S. (1996). Electronic Configurations of Superheavy Elements. J. Phys. Soc. Jpn. 65, 3175.
- Wikipedia (2015a). Alternative periodic tables.
- Wikipedia (2015b). Charles Janet.
Contact us for any suggestion or question regarding this tool.