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Divagations about the periodic table: Boolean hypercube and quantum similarity connections.

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Summary

This study explores the periodic table (PT) by linking it to Boolean hypercubes and prime atomic numbers. It also introduces quantum similarity (QS) to analyze element relationships using Gaussian atomic density functions.

Keywords:
Gaussian atomic density functionsPT as a seven-dimensional hypercubeatomic QS matrixatomic QS statistical-like parametersgraphical representation of PT atomic setsperiodic table (PT) of the elementsprime atomic numbersquantum similarity (QS)simplified atomic QS

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Area of Science:

  • Quantum Chemistry
  • Theoretical Chemistry
  • Chemical Informatics

Background:

  • The periodic table (PT) organizes elements based on recurring properties.
  • Understanding relationships between elements is crucial in chemistry.
  • Novel methods can provide deeper insights into the PT's structure.

Purpose of the Study:

  • To explore novel connections between the periodic table and mathematical structures.
  • To investigate the properties of elements with prime atomic numbers.
  • To apply quantum similarity (QS) for a new perspective on element relationships.

Main Methods:

  • Connecting the periodic table structure to a seven-dimensional Boolean hypercube.
  • Representing PT elements as quantum objects using Gaussian atomic density functions.
  • Constructing and analyzing quantum similarity (QS) matrices for PT elements.

Main Results:

  • A link is established between the periodic table and Boolean hypercube structures.
  • Elements with prime atomic numbers are analyzed within this framework.
  • Quantum similarity (QS) matrices provide a quantitative method to represent and analyze element relationships.

Conclusions:

  • The study offers a novel mathematical and quantum-based perspective on the periodic table.
  • Quantum similarity (QS) provides a versatile tool for analyzing element sets.
  • This approach allows for numerical and graphical representation of atomic element sets.