Challenges for the Periodic Systems of Elements: Chemical, Historical and Mathematical Perspectives

Area of Science:

• Chemistry
• Chemical Physics
• Theoretical Chemistry

Background:

• Periodic systems originated in the 1860s as pedagogical tools to organize elements based on similarities.
• These systems, crucial in chemistry, have evolved beyond simple tables to complex mathematical structures.
• The periodic law's universality is questioned, as it doesn't encompass all element and compound properties.

Purpose of the Study:

• To critically assess the current state and limitations of periodic systems after 150 years.
• To explore the mathematical structure of periodic systems using hypergraphs.
• To propose a renewed approach for periodic systems by reintegrating chemical space and compound information.

Main Methods:

• Generalizing periodic systems as ordered hypergraphs to define their mathematical structure.
• Analyzing current challenges in periodic systems, including order reversals in super-heavy elements and predictive power limitations.
• Investigating the extension of periodic systems into extreme regions like super-heavy atoms and antimatter.

Main Results:

• Periodic systems have been successfully generalized as ordered hypergraphs, solving long-standing questions about their mathematical foundation.
• Hypergraph models show potential for resolving issues like order reversals in super-heavy elements and enhancing predictive capabilities.
• The study identifies oversimplifications in current systems, particularly the myth of vertical group similarity, stemming from 20th-century projections of 19th-century concepts.

Conclusions:

• Periodic systems require a fundamental re-evaluation, moving beyond simplistic element-based tables to incorporate the complexity of chemical space.
• The generalization into hypergraphs offers a robust mathematical framework to address current limitations and extend the predictive power of periodic systems.
• Reintroducing chemical and compound information is essential to revitalize periodic systems and ensure their continued relevance in modern chemistry.