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  Web Book Home Page | Chemogenesis Main Index Foreword:  Chemogenesis & Chemical Education Part I   Atoms | Elements | Periodic Tables 1.1  Introduction to Chemogenesis 1.2  Nucleosynthesis of The Elements 1.3  The Segrè Chart 1.4  Quantum Numbers to Periodic Tables 1.5  The Periodic Table: What Is It Showing? 1.6  The INTERNET Database of Periodic Tables 1.7  Periodicity Part II   Structure | Bonding | Material Type 2.1  Mono-Bond Typed Binary Compounds 2.2  Binary Compound Synthlet 2.3  Electronegativity 2.4  van Arkel-Ketelaar Triangles of Bonding 2.5  Tetrahedra of Structure, Bonding & Material Type 2.6  Structure, Bonding & Material Synthlet 2.7  The Classification of Matter: Chemical Stuff Part III   Interactions | Reactions | Mechanisms 3.1  The Chemogenesis Analysis: An Overview 3.2  Lewis and Brønsted Models of Acidity 3.3  The Hard Soft [Lewis] Acid Base Principle 3.4  Main Group Elemental Hydrides 3.5  Five Hydrogen Probe Experiments 3.6  Congeneric Dots, Series & Planars 3.7  Quantifying Congeneric Behaviour 3.8  Ligand Replacement Congeneric Series 3.9  Congeneric Array Interactions 3.10  Emergence of Organic Chemistry 3.11  Congeneric Array Database 3.12  The Five Reaction Chemistries 3.13  Lewis Acids & Lewis Bases: A New Analysis 3.14  The Lewis Acid/Base Interaction Matrix 3.15  Patterns in Reaction Chemistry Poster 3.16  Lewis Acid/Base Interaction Matrix Database 3.17  Nucleophiles, Bases & The Fluoride Ion 3.18  Redox Chemistry 3.19  Redox Chemistry Synthlet 3.20  Radical Chemistry 3.21  Diradical Chemistry 3.22  Photochemistry 3.23  Species/Species Interactions 3.24  The Simplest Mechanistic Step: STAD 3.25  Unit & Compound Mechanistic Steps 3.26  The Mechanism Matrix 3.27  Addition To A Double Bond Synthlet 3.28  Pericyclic Reaction Chemistry Part IV   Chemical Theory 4.1  Why Do Chemical Reactions Occur? 4.2a  Thermochemistry: List Reactions Synthlet 4.2b  Thermochemistry: Play With Reaction Synthlet 4.2c  Thermochemistry: Bulid A Reaction Synthlet 4.3  Timeline of Structural Theory 4.4  Modern Lewis Theory 4.5  Valence Shell Electron Pair Repulsion: VSEPR 4.6  Diatomic Species by Molecular Orbital Theory 4.7  Polyatomic Species: Molecular Orbitals 4.8  Organic π-Systems 4.9  Functional Group Database Part V   Complexity & Emergence 5.1  Chemistry & Complexity: Systems 5.2  Linear Chemistry Systems 5.3  Chemical Systems Prone to Complexity Part VI   Extras 6.1  Chemogenesis Videos 6.2  Chemical Thesaurus Reaction Chemistry Database 6.3  Paper: Chemogenesis 6.4  Paper: Electronegativity as a Basic Elemental Property (FoC) 6.5  Workshop: What is Chemistry? 6.6  Paper: Scientific laws, Dalton’s postulates, chemical reactions
          and Wolfram’s NKS (FoC) 6.7  Literature References & Further Reading

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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. The database holds information on periodic tables, the discovery of the elements, the elucidation of atomic weights and the discovery of atomic structure (and much, much more).

Emergent Helicoidal Manifold Periodic Table

The Periodic Table as an Emergent Helicoidal Manifold: A Unified Information-Theoretic Analysis of the Atomic Elements Z = 1–10, by R.O. Esquivel, Quantum Rep. 2026, 8, 22 https://doi.org/10.3390/quantum8010022

Abstract

Here we perform a detailed information-theoretic (IT) analysis of atomic electron densities in the periodic table, from hydrogen (Z = 1) to lawrencium (Z = 103). By use of the Shannon entropy, the Fisher information and the disequilibrium functionals in both position and momentum spaces as fundamental descriptors of the atomic densities, the periodic table can be represented in a three-dimensional information space as a continuous, highly ordered manifold. The analysis shows that chemical periodicity naturally emerges as a helicoidal manifold (reminiscent of a helix) at the coordinates of a 3D theoretic-information space (Shannon, Fisher, Disequilibrium), with each period forming one segment within the continuous global trajectory. We find information-theoretic signatures of shell structure, sub-shell filling, and electron-configuration anomalies, such as the familiar irregularities seen in chromium and copper. Therefore, the helicoidal character emerges naturally and is not imposed a priori. 

Thanks to Eric Scerri for the tip!

© Mark R. Leach Ph.D. 1999 –

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