This research is devoted to study the evolution of the periodic system of chemical elements and to analyse its mathematical underpinnings. Therefore, it considers historical aspects of the periodic system with particular emphasis on the interplay between the expansion of the chemical space, spanned by all known chemical substances, and the resulting periodic system. Hence, our approach is also data-driven. We have analysed the robustness of the periodic system regarding different characterisations of the chemical elements, for example using chemical substances associated to each element or physicochemical elemental properties. The mathematical component in this research is evident in the mathematical theories and concepts used to treat the periodic system, ranging from topology, network theory to category theory and hypergraphs. The study of the mathematical structure of the periodic system of chemical elements has led us to formulate a general structure for periodic systems, in general, not only of chemical interest but of possible appearance in other scientific disciplines.
So far this research has been conducted by scientists at the Max Planck Institute for Mathematics in the Sciences and Leipzig University, but we are open to further collaboration with scientists and scholars of other institutions. There are also several research projects available for MSc and PhD students, as well as for postdocs.
Questions related to this research topic can be addressed to Guillermo Restrepo at restrepo@mis.mpg.de or guillermorestrepo@gmail.com.
References:
Leal, W.; Llanos, E. J.; Bernal, A.; Stadler, P. F.; Jost, J.; Restrepo, G. The expansion of chemical space in 1826 and in the 1840s prompted the convergence to the periodic system. P. Natl. Acad. Sci. USA 2022, 119, e2119083119 .
Restrepo, G. Zeit für eine neue Ordnung? Spektrum der Wissenschaft, 2022, 12th April.
Restrepo, G. Das periodische System und die Evolution des chemischen Raums. Nachr. Chem. 2020, https://doi-org.ezproxy.mis.mpg.de/10.1002/nadc.20204094740.
Restrepo, G. Challenges for the periodic systems of elements: chemical, historical and mathematical perspectives. Chem. Eur. J. 2019, 25, 15430.
Restrepo, G. Compounds bring back chemistry to the system of chemical elements. Substantia. 2019, 3, DOI: 10.13128/Substantia-739.
Leal, W.; Restrepo, G. Formal structure of periodic system of elements. Proc. R. Soc. A 2019, 475: 20180581.
Mendeleev to Oganesson: A Multidisciplinary Perspective on the Periodic Table, Scerri, E.; Restrepo, G., Eds.; Oxford University Press: New York, USA, 2017.
Restrepo, G. The Periodic System: A Mathematical Approach. In: Mendeleev to Oganesson: A Multidisciplinary Perspective on the Periodic Table, Scerri, E.; Restrepo, G., Eds.; Oxford University Press: New York, USA, 2017.
Restrepo, G. Building classes of similar chemical elements from binary compounds and their stoichiometries. In: Elements Old and New: Discoveries, Developments, Challenges, and Environmental Implications, Benvenuto, M. A.; Williamson, T., Eds.; ACS Symposium Series; American Chemical Society; Washington, DC, USA, 2017; Chapter 5, 95-110.
Restrepo, G. Una mirada a la estructura de semejanzas del sistema periódico de los elementos químicos. In: Un Festschriftt para José Luis Villaveces, Arboleda, L. C., Ed.; Academia Colombiana de Ciencias Exactas, Físicas y Naturales: Bogota, Colombia, 2017.
Bernal, A.; Llanos, E.; Leal, W.; Restrepo, G. Similarity in Chemical Reaction Networks: Categories, Concepts and Closures. In Advances in mathematical chemistry and applications, Basak, S. C.; Restrepo, G.; Villaveces, J. L., Eds.; Bentham: Sharjah, UAE, 2015; Chapter 2, 24-54.
Leal, W.; Restrepo, G.; Bernal, A. A network study of chemical elements: from binary compounds to chemical trends. MATCH Commun. Math. Comput. Chem. 2012, 68, 417-442.
Restrepo, G.; Pachón, L. Mathematical aspects of the periodic law. Found. Chem. 2007, 9, 189-214.
Restrepo, G.; Llanos, E. J.; Mesa, H. Topological space of the chemical elements and its properties. J. Math. Chem. 2006, 39, 401-416.
Restrepo, G.; Mesa, H.; Llanos, E. J.; Villaveces, J. L. Topological study of the periodic system. In The mathematics of the periodic table; King, B.; Rouvray, D., Eds.; Nova: New York, USA, 2006; Chapter 5, 75-100.
Restrepo, G.; Mesa, H.; Llanos, E. J.; Villaveces, J. L. Topological study of the periodic system. J. Chem. Inf. Comput. Sci. 2004, 44, 68-75.